Studies in Topology - 1st Edition - ISBN: 9780126634501, 9781483259116

Studies in Topology

1st Edition

Editors: Nick M. Stavrakas Keith R. Allen
eBook ISBN: 9781483259116
Imprint: Academic Press
Published Date: 1st January 1975
Page Count: 672
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Description

Studies in Topology is a compendium of papers dealing with a broad portion of the topological spectrum, such as in shape theory and in infinite dimensional topology. One paper discusses an approach to proper shape theory modeled on the "ANR-systems" of Mardesic-Segal, on the "mutations" of Fox, or on the "shapings" of Mardesic. Some papers discuss homotopy and cohomology groups in shape theory, the structure of superspace, on o-semimetrizable spaces, as well as connected sets that have one or more disconnection properties. One paper examines "weak" compactness, considered as either a strengthening of absolute closure or a weakening of relative compactness (subject to entire topological spaces or to subspaces of larger spaces). To construct spaces that have only weak properties, the investigator can use the various productivity theorems of Scarborough and Stone, Saks and Stephenson, Frolik, Booth, and Hechler. Another paper analyzes the relationship between "normal Moore space conjecture" and productivity of normality in Moore spaces. The compendium is suitable for mathematicians, physicists, engineers, and other professionals involved in topology, set theory, linear spaces, or cartography.

Table of Contents


Contributors

Preface

Acknowledgments

Birth of The Polish School of Mathematics

Alternative Approaches to Proper Shape Theory

On the Existence and Uniqueness Theorems of R. S. Pierce for Extensions of Zero-Dimensional Compact Metric Spaces

Mapping Continua onto the Cone over the Cantor Set

Nearness Spaces and Extensions of Topologicai Spaces

On Several Problems of the Theory of Shape

Some Results on (E, βE)—Compactness

Torodial Decompositions of Manifolds Yield Factors of Manifolds

Homotopy and Cohomology Groups in Shape Theory

The Structure of Superspace

Some Notes on Multifunctions

Connected Sets with a Finite Disconnection Property

Applications of Collectionwise Hausdorff

On 0-Semimetrizable Spaces

Characterizing Topological Properties by Real Functions

λ Connectivity in the Plane

On Continuous Extenders

On a Notion of Weak Compactness in Non-Regular Spaces

Actions of Locally Compact Groups with Zero on Manifolds

Non-Continuous Retracts

The Nielsen Numbers and Fiberings

Maps of ANR's Determined on Null Sequence of AR's

Two Vietoris-Type Isomorphism Theorems in Borsuk's Theory of Shape, Concerning the Vietoris-Cech Homology and Borsuk's Fundamental Groups

Uniformly Pathwise Connected Continua

Several Problems of Continua Theory

A Characterization of Local Connectivity in Dendroids

A Survey of Embedding Theorems for Semigroups of Continuous Functions

The Hurewicz and Whitehead Theorems in Shape Theory

One-Dimensional Shape Properties and Three-Manifolds

Discontinuous Gδ Graphs

Some Basic Connectivity Properties of Whitney Map Inverses in C(X)

One-Point Compactifications of Q-Manifold Factors and Infinite Mapping Cylinders

Some Surprising Base Properties in Topology

Some Topological Questions Related to Open and Closed Graph Theorems

Completeness in Aronszajn Spaces

Projectives in the Category of Ordered Spaces

On the Productivity of Normality in Moore Spaces

A Metrization Theorem for Normal Moore Spaces

Extensions of Topologies by Locally Finite Collections

Some Approximation Theorems for Inverse Limits

The Metrizability of Normal Moore Spaces

Toward a Product Theory for Orthocompactness

Movable Continua and Shape Retracts

n-adic Decompositions and Retracts

Embedding Characterizations for Collectionwise Normality and Expandibility

Extending Maps from Products

Dense Subsemigroups of Semigroups of Continuous Selfmaps

Banach Spaces with Banach-Stone Property

Primitive Structures in General Topology

Recent Developments in Dendritic Spaces and Related Topics

Index

Details

No. of pages:
672
Language:
English
Copyright:
© Academic Press 1975
Published:
Imprint:
Academic Press
eBook ISBN:
9781483259116

About the Editor

Nick M. Stavrakas

Keith R. Allen