A Survey on Almost 0-Dimensional Spaces
by
Kazuhiro Kawamura

A separable metrizable space X is said to be almost zero-dimensional if there exists a countable base B of X which satisfies the following property:

• for each pair B₁, B₂ in B such that clB₁ \cap clB₂ = \emptyset, there exists a clopen set G of X suvh that B₁ subset G and B₂ subset X-G.

It is easy to see the following implications.

zero-dimensional \implies almost zero dimensional \implies totally disconnected.

The concept of almost zero-dimensionality was introduced by L. G. Oversteegen and E. D. Tymchatyn. It provides a convenient viewpoint on the study of totally disconnected (at most) one-dimensional spaces. In this talk, we give a survey on the topic and some open questions are proposed.

Date received: June 24, 1996

Copyright © 1996 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Mathematical Conference Abstracts. Document # caaj-36.