Continuous Images Of Arcs And Inverse Limit Methods

Author : Jacek Nikiel,H. M. Tuncali,E. D. Tymchatyn
Publisher : American Mathematical Soc.
Page : 80 pages
File Size : 48,9 Mb
Release : 1993
Category : Mathematics
ISBN : 9780821825617

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Continuous Images of Arcs and Inverse Limit Methods by Jacek Nikiel,H. M. Tuncali,E. D. Tymchatyn Pdf

Continuous images of ordered continua have been studied intensively since 1960, when S. Mardsic showed that the classical Hahn-Mazurkiewicz theorem does not generalize in the ``natural'' way to the nonmetric case. In 1986, Nikiel characterized acyclic images of arcs as continua which can be approximated from within by a sequence of well-placed subsets which he called T-sets. That characterization has been used to answer a host of outstanding questions in the area. In this book, Nikiel, Tymchatyn, and Tuncali study images of arcs using T-set approximations and inverse limits with monotone bonding maps. A number of important theorems on Peano continua are extended to images of arcs. Some of the results presented here are new even in the metric case.

Author : Jacek Nikiel
Publisher : Oxford University Press, USA
Page : 95 pages
File Size : 45,9 Mb
Release : 2014-08-31
Category : MATHEMATICS
ISBN : 1470400758

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Continuous Images of Arcs and Inverse Limit Methods by Jacek Nikiel Pdf

Continuous images of ordered continua have been studied intensively since 1960, when S. Mardvsic showed that the classical Hahn-Mazurkiewicz theorem does not generalize in the natural way to the nonmetric case. In 1986, Nikiel characterized acyclic images of arcs as continua which can be approximated from within by a sequence of well-placed subsets which he called T-sets. That characterization has been used to answer a host of outstanding questions in the area. In this book, Nikiel, Tymchatyn and Tuncali study images of arcs using T-set approximations and inverse limits with monotone bonding maps. A number of important theorems on Peano continua are extended to images of arcs.

Author : M. Husek,J. van Mill
Publisher : Elsevier
Page : 808 pages
File Size : 44,6 Mb
Release : 1992-11-20
Category : Mathematics
ISBN : 9780080934433

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Recent Progress in General Topology by M. Husek,J. van Mill Pdf

These papers survey the developments in General Topology and the applications of it which have taken place since the mid 1980s. The book may be regarded as an update of some of the papers in the Handbook of Set-Theoretic Topology (eds. Kunen/Vaughan, North-Holland, 1984), which gives an almost complete picture of the state of the art of Set Theoretic Topology before 1984. In the present volume several important developments are surveyed that surfaced in the period 1984-1991. This volume may also be regarded as a partial update of Open Problems in Topology (eds. van Mill/Reed, North-Holland, 1990). Solutions to some of the original 1100 open problems are discussed and new problems are posed.

Author : Svante Janson
Publisher : American Mathematical Soc.
Page : 78 pages
File Size : 46,8 Mb
Release : 1994
Category : Mathematics
ISBN : 9780821825952

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Orthogonal Decompositions and Functional Limit Theorems for Random Graph Statistics by Svante Janson Pdf

This book develops a method to obtain limit theorems for various functionals of random graphs. The method is based on a certain orthogonal decomposition. Janson's results include limit theorems for the two standard random graph models, $G_{n,p}$ and $G_{n,m}$, as well as functional limit theorems for the evolution of a random graph and results on the maximum of a function during the evolution. Janson obtains both normal and nonnormal limits, and the method provides an explanation for the appearance of nonnormal limits. Applications to subgraph counts and to vertex degrees are presented as examples.

Author : Hongbing Su
Publisher : American Mathematical Soc.
Page : 83 pages
File Size : 49,7 Mb
Release : 1995
Category : Mathematics
ISBN : 9780821826072

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On the Classification of $C^*$-algebras of Real Rank Zero: Inductive Limits of Matrix Algebras over Non-Hausdorff Graphs by Hongbing Su Pdf

This work shows that $K$-theoretic data is a complete invariant for certain inductive limit $C^*$-algebras. $C^*$-algebras of this kind are useful in studying group actions. Su gives a $K$-theoretic classification of the real rank zero $C^*$-algebras that can be expressed as inductive limits of finite direct sums of matrix algebras over finite (possibly non-Hausdorff) graphs or Hausdorff one-dimensional spaces defined as inverse limits of finite graphs. In addition, Su establishes a characterization for an inductive limit of finite direct sums of matrix algebras over finite (possibly non-Hausdorff) graphs to be real rank zero.

Author : Krzysztof Ciesielski,Lee Larson,Krzysztof Ostaszewski
Publisher : American Mathematical Soc.
Page : 133 pages
File Size : 52,7 Mb
Release : 1994
Category : Mathematics
ISBN : 9780821825792

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I-Density Continuous Functions by Krzysztof Ciesielski,Lee Larson,Krzysztof Ostaszewski Pdf

The classical approach to showing the parallel between theorems concerning Lebesgue measure and theorems concerning Baire category on the real line is restricted to sets of measure zero and sets of first category. This is because classical Baire category theory does not have an analogue for the Lebesgue density theorem. By using {mathcal I}-density, this deficiency is removed, and much of the structure of measurable sets and functions can be shown to exist in the sense of category as well. This monograph explores category analogues to such things as the density topology, approximate continuity, and density continuity. In addition, some questions about topological semigroups of real functions are answered.

Author : Eriko Hironaka
Publisher : American Mathematical Soc.
Page : 98 pages
File Size : 48,5 Mb
Release : 1993
Category : Algebraic varieties
ISBN : 9780821825648

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Abelian Coverings of the Complex Projective Plane Branched along Configurations of Real Lines by Eriko Hironaka Pdf

This work studies abelian branched coverings of smooth complex projective surfaces from the topological viewpoint. Geometric information about the coverings (such as the first Betti numbers of a smooth model or intersections of embedded curves) is related to topological and combinatorial information about the base space and branch locus. Special attention is given to examples in which the base space is the complex projective plane and the branch locus is a configuration of lines.

Author : K.P. Hart,Jun-iti Nagata,J.E. Vaughan
Publisher : Elsevier
Page : 537 pages
File Size : 52,9 Mb
Release : 2003-11-18
Category : Mathematics
ISBN : 9780080530864

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Encyclopedia of General Topology by K.P. Hart,Jun-iti Nagata,J.E. Vaughan Pdf

This book is designed for the reader who wants to get a general view of the terminology of General Topology with minimal time and effort. The reader, whom we assume to have only a rudimentary knowledge of set theory, algebra and analysis, will be able to find what they want if they will properly use the index. However, this book contains very few proofs and the reader who wants to study more systematically will find sufficiently many references in the book. Key features: • More terms from General Topology than any other book ever published• Short and informative articles• Authors include the majority of top researchers in the field• Extensive indexing of terms

Author : Alouf Jirari
Publisher : American Mathematical Soc.
Page : 138 pages
File Size : 48,8 Mb
Release : 1995
Category : Mathematics
ISBN : 9780821803592

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Second-Order Sturm-Liouville Difference Equations and Orthogonal Polynomials by Alouf Jirari Pdf

This well-written book is a timely and significant contribution to the understanding of difference equations. Presenting machinery for analyzing many discrete physical situations, the book will be of interest to physicists and engineers as well as mathematicians. The book develops a theory for regular and singular Sturm-Liouville boundary value problems for difference equations, generalizing many of the known results for differential equations. Discussing the self-adjointness of these problems as well as their abstract spectral resolution in the appropriate $L^2$ setting, the book gives necessary and sufficient conditions for a second-order difference operator to be self-adjoint and have orthogonal polynomials as eigenfunctions. These polynomials are classified into four categories, each of which is given a properties survey and a representative example. Finally, the book shows that the various difference operators defined for these problems are still self-adjoint when restricted to ``energy norms''. This book is suitable as a text for an advanced graduate course on Sturm-Liouville operators or on applied analysis.

Author : Shirō Gotō,Koji Nishida
Publisher : American Mathematical Soc.
Page : 134 pages
File Size : 52,8 Mb
Release : 1994
Category : Mathematics
ISBN : 9780821825846

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The Cohen-Macaulay and Gorenstein Rees Algebras Associated to Filtrations by Shirō Gotō,Koji Nishida Pdf

This monograph consists of two parts. Part I investigates the Cohen-Macaulay and Gorenstein properties of symbolic Rees algebras for one-dimensional prime ideals in Cohen-Macaulay local rings. Practical criteria for these algebras to be Cohen-Macaulay and Gorenstein rings are described in terms of certain elements in the prime ideals. This framework is generalized in Part II to Rees algebras $R(F)$ and graded rings $G(F)$ associated to general filtrations of ideals in arbitrary Noetherian local rings. Goto and Nishida give certain cohomological characterizations for algebras $R(F)$ to be Cohen-Macaulay or Gorenstein rings in connection with the corresponding ring-theoretic properties of $G(F)$. In this way, readers follow a history of the development of the ring theory of Rees algebras. The book raises many important open questions.

Author : Christian Krattenthaler
Publisher : American Mathematical Soc.
Page : 109 pages
File Size : 43,9 Mb
Release : 1995
Category : Mathematics
ISBN : 9780821826133

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The Major Counting of Nonintersecting Lattice Paths and Generating Functions for Tableaux by Christian Krattenthaler Pdf

This work develops a theory for counting nonintersecting lattice paths by the major index and generalizations of it. As applications, Krattenthaler computes certain tableaux and plane partition generating functions. In particular, he derives refinements of the Bender-Knuth and McMahon conjectures, thereby giving new proofs of these conjectures. Providing refinements of famous results in plane partition theory, this work combines in an effective and nontrivial way classical tools from bijective combinatorics and the theory of special functions.

Author : Giora Dula,Reinhard Schultz
Publisher : American Mathematical Soc.
Page : 82 pages
File Size : 46,8 Mb
Release : 1994
Category : Mathematics
ISBN : 9780821825891

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Diagram Cohomology and Isovariant Homotopy Theory by Giora Dula,Reinhard Schultz Pdf

In algebraic topology, obstruction theory provides a way to study homotopy classes of continuous maps in terms of cohomology groups; a similar theory exists for certain spaces with group actions and maps that are compatible (that is, equivariant) with respect to the group actions. This work provides a corresponding setting for certain spaces with group actions and maps that are compatible in a stronger sense, called isovariant. The basic idea is to establish an equivalence between isovariant homotopy and equivariant homotopy for certain categories of diagrams. Consequences include isovariant versions of the usual Whitehead theorems for recognizing homotopy equivalences, an obstruction theory for deforming equivariant maps to isovariant maps, rational computations for the homotopy groups of certain spaces of isovariant functions, and applications to constructions and classification problems for differentiable group actions.

Author : Neal W. Stoltzfus
Publisher : American Mathematical Soc.
Page : 91 pages
File Size : 43,8 Mb
Release : 1977
Category : Mathematics
ISBN : 9780821821923

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Unraveling the Integral Knot Concordance Group by Neal W. Stoltzfus Pdf

The group of concordance classes of high dimensional homotopy spheres knotted in codimension two in the standard sphere has an intricate algebraic structure which this paper unravels. The first level of invariants is given by the classical Alexander polynomial. By means of a transfer construction, the integral Seifert matrices of knots whose Alexander polynomial is a power of a fixed irreducible polynomial are related to forms with the appropriate Hermitian symmetry on torsion free modules over an order in the algebraic number field determined by the Alexander polynomial. This group is then explicitly computed in terms of standard arithmetic invariants. In the symmetric case, this computation shows there are no elements of order four with an irreducible Alexander polynomial. Furthermore, the order is not necessarily Dedekind and non-projective modules can occur. The second level of invariants is given by constructing an exact sequence relating the global concordance group to the individual pieces described above. The integral concordance group is then computed by a localization exact sequence relating it to the rational group computed by J. Levine and a group of torsion linking forms.

Author : Victor Guillemin,Shlomo Sternberg
Publisher : American Mathematical Soc.
Page : 80 pages
File Size : 42,6 Mb
Release : 1966
Category : Mathematics
ISBN : 9780821812648

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Deformation Theory of Pseudogroup Structures by Victor Guillemin,Shlomo Sternberg Pdf

Author : Huaxin Lin
Publisher : American Mathematical Soc.
Page : 89 pages
File Size : 42,8 Mb
Release : 1995
Category : Mathematics
ISBN : 9780821826119

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$C^*$-Algebra Extensions of $C(X)$ by Huaxin Lin Pdf

This work shows that the Weyl-von Neumann theorem for unitaries holds for $\sigma$-unital $AF$-algebras and their multiplier algebras. Lin studies $E(X,A)$, the quotient of $\mathrm{{\mathbf{Ext}}}^{eu}_s(C(X),A)$ by a special class of trivial extension, dubbed totally trivial extensions. This leads to a BDF-type classification for extensions of $C(X)$ by a $\sigma$-unital purely infinite simple $C^*$-algebra with trivial $K_1$-group. Lin also shows that, when $X$ is a compact subset of the plane, every extension of $C(X)$ by a finite matroid $C^*$-algebra is totally trivial. Classification of these extensions for nice spaces is given, as are some other versions of the Weyl-von Neumann-Berg theorem.