An operation on topological spaces

Authors

  • A. V. Arhangelskii Ohio University

DOI:

https://doi.org/10.4995/agt.2000.3021

Keywords:

C-embedding, Diagonalizable space, Hewitt-Nachbin completion, Moscow space, Pseudocompact space, Separability, Tightness

Abstract

A (binary) product operation on a topological space X is considered. The only restrictions are that some element e of X is a left and a right identity with respect to this multiplication, and that certain natural continuity requirements are satisfied. The operation is called diagonalization (of X). Two problems are considered: 1. When a topological space X admits such an operation, that is, when X is diagonalizable? 2. What are necessary conditions for diagonalizablity of a space (at a given point)? A progress is made in the article on both questions. In particular, it is shown that certain deep results about the topological structure of compact topological groups can be extended to diagonalizable compact spaces. The notion of a Moscow space is instrumental in our study.

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Author Biography

A. V. Arhangelskii, Ohio University

Department of Mathematics

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Published

2000-10-01

How to Cite

[1]
A. V. Arhangelskii, “An operation on topological spaces”, Appl. Gen. Topol., vol. 1, no. 1, pp. 13–28, Oct. 2000.

Issue

Section

Regular Articles