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On the Structure of Finite T0 + T5 Spaces

Published online by Cambridge University Press:  20 November 2018

Shawpawn Kumar Das
Shawpawn Kumar Das*
Affiliation:
10 Raja Dinendra Street, Calcutta, 700009, India
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The object of this paper is to study some structural aspects of finite T0 + T4 and T0 + T5 spaces in order to establish certain recursion relations that can be used to obtain the number of (labelled as well as unlabelled) T0 + T5 topologies on a finite set.Here, as in [2], a topology 𝒥 is a T4(T5) space provided for any pair of disjoint closed sets A and B (separated sets A and B = A ∩ closure B = B ∩ closure A = 0) there exist disjoint open sets 0A and 0B 𝒥 such that A ⊆ 0A and B ⊆ 0B. An almost immediate consequence of these investigations is that the inherent simplicity of the connected T0 + T5 topologies ensures that they are reconstructable.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 25 , Issue 6 , December 1973 , pp. 1148 - 1158
Copyright
Copyright © Canadian Mathematical Society 1973

References

1. Das, Shawpawn Kumar, A partition of finite T0 topologies, Can. J. Math. 25 (1973), 1137–1147.Google Scholar
2. Gaal, S. A., Point set topology (Academic Press, New York, 1964).Google Scholar