Dimension Theory of General Spaces

A complete and self-contained account of the dimension theory of general topological spaces, with particular emphasis on the dimensional properties of non-metrizable spaces.

A. R. Pears (Author)

9780521093026, Cambridge University Press

Paperback / softback, published 8 January 2009

444 pages
22.9 x 15.2 x 2.5 cm, 0.65 kg

A complete and self-contained account of the dimension theory of general topological spaces, with particular emphasis on the dimensional properties of non-metrizable spaces. It makes the subject accessible to beginning graduate students and will also serve as a reference work for general topologists. Two introductory chapters summarize standard results in general topology, and cover material on paracompactness and metrization. The principal definitions of dimension follow and their general properties are deduced. Many examples are analysed to show some of the more surprising or pathological aspects of dimension theory. Wherever it is useful to do so, proofs are given in detail.

1. Topological spaces, normality and compactness
2. Paracompact and pseudo- metrizable spaces
3. Covering dimension
4. Inductive dimension
5. Local dimension
6. Images of zero-dimensional spaces
7. The dimension of pseudo-metrizable and metrizable spaces
8. The dimension of bicompact spaces.

Subject Areas: Mathematics [PB]