Note on hit-and-miss topologies |
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Authors: | László Zsilinszky |
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Institution: | (1) Department of Mathematics and Computer Science, University of North Carolina at Pembroke, 28372 Pembroke, NC, USA |
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Abstract: | This is a continuation of 19]. We characterize first and second countability of the general hit-and-miss hyperspace topologyτ
+
Δ
for weakly-R
0 base spaces. Further, metrizability ofτ
+
Δ
is characterized with no preliminary conditions on the base space and the generating family of closed sets and a new proof
on uniformizability (i.e. complete regularity) ofτ
+
Δ
is given in this general setting, thus generalizing results of 3], 5] and 6]. |
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Keywords: | 1991 Mathematics Subject Classification" target="_blank">1991 Mathematics Subject Classification 54B20 Secondary 54D15 54E35 |
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