On low dimensional KC-spaces

2011/03/01 by Fabel, Paul
#54F50 #FOS: Mathematics #General Topology (math.GN)

paper · doi:10.48550/arxiv.1103.0256

Abstract

The KC property, a separation axiom between weakly Hausdorff and Hausdorff, requires compact subsets to be closed. Various assumptions involving local conditions, dimension, connectivity, and homotopy show certain KC-spaces are in fact Hausdorff. Several low dimensional examples of compact, connected, non-Hausdorff KC-spaces are exhibited in which the nested intersection of compact connected subsets fails to be connected.

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