Dissipated Compacta

2007/03/14 by Kenneth Kunen, Kunen, Kenneth
Mathematics · #54D30 #54F05 #FOS: Mathematics #General Topology (math.GN) #math.GN #msc:54D30 #msc:54F05

paper · pdf · doi:10.48550/arxiv.math/0703429

34 pages

arxiv created 2007/03/14 · arxiv updated 2009/12/01

Abstract

The dissipated spaces form a class of compacta which contains both the scattered compacta and the compact LOTSes (linearly ordered topological spaces), and a number of theorems true for these latter two classes are true more generally for the dissipated spaces. For example, every regular Borel measure on a dissipated space is separable. A product of two compact LOTSes is usually not dissipated, but it may satisfy a weakening of that property. In fact, the degree of dissipation of a space can be used to distinguish topologically a product of n LOTSes from a product of m LOTSes.

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