Normal Topological Spaces

This text bridges the gap existing in the field of set theoretical topology between the introductory texts and the more specialized monographs.

Richard A. Alo (Author), Harvey L. Shapiro (Author)

9780521095303, Cambridge University Press

Paperback / softback, published 11 January 2009

320 pages
21.6 x 14 x 1.8 cm, 0.41 kg

This text bridges the gap existing in the field of set theoretical topology between the introductory texts and the more specialised monographs. The authors review fit developments in general topology and discuss important new areas of research and the importance of defining a methodology applicable to this active field of mathematics. The concept of normal cover and related ideas is considered in detail, as are the characterisations of normal spaces, collectionwise normal spaces and their interrelationships with paracompact spaces (and other weaker forms of compactness). Various methods of embedding subspaces are studied, before considering newer concepts such as M-spaces and their relationships with established ideas. These ideas are applied to give new results pertaining to the extension of continuous vector-valued functions. Wallman–Frink compactifications and realcompactifications are also studied to assist in unifying the ideas through the use of the more general L-filter.

1. Preliminaries
2. Normality and real-valued continuous functions
3. Normality and normal covers
4. Normality and pseudometrics
5. Normality and uniformities.

Subject Areas: Geometry [PBM]