Abstract. Regular and irregular pretopologies are studied. In particular, for every ordinal there exists a topology such that the series of its partial (pretopological) regularizations has length of that ordinal. Regularity and topologicity of standard pretopologies on cascades can be characterized in terms of their states, so that their study for such spaces reduces to that of a combinatorics of states. For example, if an iterated partial regularization r^kpi is topological for k > 0 then rpi is a regular topology. Irregularity of pretopologies of countable character can be characterized in terms of sequential cascades with standard irregular pretopologies. |
Keywords
convergence spaces, pretopologies, partial regularisation, cascades
Math Review Classification
Primary 54A20, 54D10
Last Updated
13/7/5
Length
26 pages
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