Dissipated Compacta

Details Dissipated Compacta Dissipated Compacta

2007-03-14

arxiv.org/abs/math/0703429v1

Mathematics

General Topology

34 pages

Scientific paper

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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