A short note on hit-and-miss hyperspaces

René Bartsch

Germany

Rostock University

Dept. of Computer Science

Harry Poppe

Germany

Rostock University

Dept. of Mathematics
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Accepted: 2013-12-16

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Published: 2003-10-01

DOI: https://doi.org/10.4995/agt.2003.2033
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Keywords:

Hit-and-miss topology, Compactness, Relative completeness, Relative compact unions, Upper Vietoris topology

Supporting agencies:

This research was not funded

Abstract:

Based on some set-theoretical observations, compactness results are given for general hit-and-miss hyperspaces. Compactness here is sometimes viewed splitting into “κ-Lindelöfness” and “κ-compactness” for cardinals κ. To focus only hit-and-miss structures, could look quite old-fashioned, but some importance, at least for the techniques, is given by a recent result, [8], of Som Naimpally, to who this article is hearty dedicated.

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References:

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Poppe, H., Eine Bemerkung über Trennungsaxiome in Räumen von abgeschlossenen Teilmengen topologischer Räume, Arch.Math. 16 (1965), 197-199. http://dx.doi.org/10.1007/BF01220021

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