Parthasarathy, shift-compactness and infinite combinatorics

Bingham, N. H. and Ostaszewski, Adam ORCID: 0000-0003-2630-8663 (2024) Parthasarathy, shift-compactness and infinite combinatorics. Indian Journal of Pure and Applied Mathematics, 55 (3). 931 – 948. ISSN 0019-5588

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Abstract

Parthasarathy’s heritage has a hidden component arising from a variant of his concept of shift-compactness which yields quick proofs of fundamental theorems reviewed here. We demonstrate the closeness of the variant notion to his original one as arising in the tacit treatment of all possible convergent centrings. We also include a very short proof of the Effros Mapping Theorem –a non-linear version of the Open Mapping Theorem. This is deduced from a shift-compactness theorem. Both these can be given a constructive form by implementing a constructive improvement to a theorem on the separation of points and closed nowhere dense sets.

Item Type:	Article
Additional Information:	© 2024 The Indian National Science Academy
Divisions:	Mathematics
Subjects:	Q Science > QA Mathematics
Date Deposited:	25 Mar 2024 14:27
Last Modified:	12 Nov 2024 23:51
URI:	http://eprints.lse.ac.uk/id/eprint/122494

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