A characterization of maximal connected spaces and maximal arcwise connected spaces

Clark, Bradd; Schneider, Victor

doi:10.1090/S0002-9939-1988-0969057-8

A characterization of maximal connected spaces and maximal arcwise connected spaces
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by Bradd Clark and Victor Schneider PDF

Proc. Amer. Math. Soc. 104 (1988), 1256-1260 Request permission

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.

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