About This Book
Topology, Volume II deals with topology and covers topics ranging from compact spaces and connected spaces to locally connected spaces, retracts, and neighborhood retracts. Group theory and some cutting problems are also discussed, along with the topology of the plane. Comprised of seven chapters, this volume begins with a discussion on the compactness of a topological space, paying particular attention to Borel, Lebesgue, Riesz, Cantor, and Bolzano-Weierstrass conditions. Semi-continuity and topics in dimension theory are also considered. The reader is then introduced to the connectedness of a space, with emphasis on the general properties and monotone mappings of connected spaces; local connectedness of a topological space; absolute retracts and contractible spaces; and general properties of commutative groups. Qualitative problems related to polygonal arcs are also examined, together with cohomotopic multiplication and duality theorems. The final chapter is devoted to the topology of a plane and evaluates the concept of the Janiszewski space. This monograph will be helpful to students and practitioners of algebra and mathematics.
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Table of contents
- Front Cover
- Topology
- Copyright Page
- Table of Contents
- Dedication
- PREFACE TO THE SECOND VOLUME
- CHAPTER FOUR. COMPACT SPACES
- CHAPTEE FIVE. CONNECTED SPACES
- CHAPTEK SIX. LOCALLY CONNECTED SPACES
- CHAPTER SEVEN. ABSOLUTE RETRACTS. SPACES CONNECTED IN DIMENSION n CONTRACTIBLE SPACES
- CHAPTER EIGHT. GROUPS
- CHAPTER NINE. SOME THEOREMS ON THE DISCONNECTION OF THE SPHERE
- CHAPTER TEN. TOPOLOGY OF THE PLANE
- List of important symbols
- Author index
- Subject index