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On the Structure of Finite T0 + T5 Spaces
Published online by Cambridge University Press:Â 20 November 2018
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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 đ„ is a T4(T5) space provided for any pair of disjoint closed sets A and B (separated sets A and B = A â© closure B = B â© closure A = 0) there exist disjoint open sets 0A and 0B đ„ such that A â 0A and B â 0B. An almost immediate consequence of these investigations is that the inherent simplicity of the connected T0 + T5 topologies ensures that they are reconstructable.
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- Copyright © Canadian Mathematical Society 1973
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