Studies in Topology

Nick M. Stavrakas, Keith R. Allen

• Publisher: Academic Press
• Year: 2014
• ISBN:
  9781483259116
• Topic: Mathematics
• Subtopic: Topology
• Index: Mathematics

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

• Front Cover
• Studies in Topology
• Copyright Page
• Table of Contents
• Contributors
• Preface
• Acknowledgments
• Birth of the Polish School of Mathematics
• Chapter 1. Alternative Approaches to Proper Shape Theory
• Chapter 2. On the Existence and Uniqueness Theorems of R. S. Pierce for Extensions of Zero-Dimensional Compact Metric Spaces
• Chapter 3. Mapping Continua Onto the Cone Over the Cantor Set
• Chapter 4. Nearness Spaces and Extensions of Topological Spaces
• Chapter 5. On Several Problems of the Theory of Shape
• Chapter 6. Some Results on (E,βE)-Compactness
• Chapter 7. Toroidal Decompositions of Manifolds Yield Factors of Manifolds
• Chapter 8. Homotopy and Cohomoiogy Groups in Shape Theory
• Chapter 9. The Structure of Superspace
• Chapter 10. Some Notes on Multifunctions
• Chapter 11. Connected Sets With a Finite Disconnection Property
• Chapter 12. Applications of Collectionwise Hausdorff
• Chapter 13. On o-semimetrizable Spaces
• Chapter 14. Characterizing Topological Properties
• Chapter 15. λ Connectivity in the Plane
• Chapter 16. On Continuous Extenders
• Chapter 17. On a Notion of Weak Compactness in Non-Regular Spaces
• Chapter 18. Actions of Locally Compact Groups With Zero on Manifolds
• Chapter 19. Non-Continuous Retracts
• Chapter 20. The Nielsen Numbers and Fiberings
• Chapter 21. Maps of ANR's Determined on Null Sequences of AR's
• Chapter 22. Two Vietoris-type isomorphism theorems in Borsuk's theory of shape, concerning the Vietoris-Cech homology and Borsuk's fundamental groups
• Chapter 23. Uniformly Pathwise Connected Continua
• Chapter 24. Several Problems of Continua Theory
• Chapter 25. A Characterization of Local Connectivity in Dendroids
• Chapter 26. A Survey of Embedding Theorems for Semigroups of Continuous Functions
• Chapter 27. THE HUREWICZ AND WHITEHEAD THEOREMS IN SHAPE THEORY
• Chapter 28. One-Dimensional Shape Properties and Three-Mamfolds
• Chapter 29. Discontinuous Gδ Graphs
• Chapter 30. Some Basic Connectivity Properties of Whitney Map Inverses in C(X)
• Chapter 31. One-Point Compactifications of Q-manifold Factors and Infinite Mapping Cylinders
• Chapter 32. Some Surprising Base Properties in Topology
• Chapter 33. Some Topological Questions Related to Open Mapping and Closed Graph Theorems
• Chapter 34. Projectives in the Category of Ordered Spaces
• Chapter 35. On the Productivity of Normality in Moore Spaces
• Chapter 36. A Metrization Theorem for Normal Moore Spaces
• Chapter 37. Expansions of Topologies by Locally Finite Collections
• Chapter 38. Some Approximation Theorems for Inverse Limits
• Chapter 39. The Metrizability of Normal Moore Spaces
• Chapter 40. Toward a Product Theory for Orthocompactness
• Chapter 41. Movable Continua and Shape Retracts
• Chapter 42. n-adic Decompositions and Retracts
• Chapter 43. Embedding Characterizations for Collectionwise Normality and Expandability
• Chapter 44. Extending Maps from Products
• Chapter 45. Dense Subsemigroups of Semigroups Of Continuous Selfmaps
• Chapter 46. Banach Spaces With Banach-Stone Property
• Chapter 47. PRIMITIVE STRUCTURES IN GENERAL TOPOLOGY
• Chapter 48. Recent Developments in Dendritic Spaces and Related Topics
• Index