A characterization of maximal connected spaces and maximal arcwise connected spaces-Reference-Cited by-同舟云学术

A characterization of maximal connected spaces and maximal arcwise connected spaces

Published:1988 Issue:4 Volume:104 Page:1256-1260
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Clark Bradd,Schneider Victor

Abstract

The concept of a maximal connected space was developed by J. P. Thomas and maximal connected expansions of the reals were discovered by Guthrie, Stone, Wage, and Simon. This paper gives necessary and sufficient conditions for a space to be maximal connected. Also necessary and sufficient conditions for the join of two connected topologies to be connected are given in the special case that one of the topologies is atomic. Finally the concept of a maximal arcwise connected topology is given and used to show that every connected simplicial complex admits both a maximal arcwise connected extension and a maximal connected extension.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/proc/1988-104-04/S0002-9939-1988-0969057-8/S0002-9939-1988-0969057-8.pdf

Reference8 articles.

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2. G. Birkoff, On the combination of topologies, Fund. Math. 26 (1936), 156-166.

3. E. Clay, Joins of Euclidean orbital topologies, Master’s Thesis, University of Southwestern Louisiana, 1986.

4. Maximal connected expansions of the reals;Guthrie, J. A.;Proc. Amer. Math. Soc.,1978

5. C. Kuratowski, Topology, vol. 1, Academic Press, New York, 1966.

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