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Axioms 2017, 6(3), 23; doi:10.3390/axioms6030023

Categorically Closed Topological Groups

1
Faculty of Mechanics and Mathematics, Ivan Franko National University, 79000 Lviv, Ukraine
2
Institute of Mathematics, Jan Kochanowski University, 25-001 Kielce, Poland
Received: 30 June 2017 / Revised: 26 July 2017 / Accepted: 27 July 2017 / Published: 30 July 2017
(This article belongs to the Collection Topological Groups)
View Full-Text   |   Download PDF [433 KB, uploaded 2 August 2017]

Abstract

Let C be a category whose objects are semigroups with topology and morphisms are closed semigroup relations, in particular, continuous homomorphisms. An object X of the category C is called C -closed if for each morphism Φ X × Y in the category C the image Φ ( X ) = { y Y : x X ( x , y ) Φ } is closed in Y. In the paper we survey existing and new results on topological groups, which are C -closed for various categories C of topologized semigroups. View Full-Text
Keywords: topological group; paratopological group; topological semigroup; absolutely closed topological group; topological group of compact exponent topological group; paratopological group; topological semigroup; absolutely closed topological group; topological group of compact exponent
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Banakh, T. Categorically Closed Topological Groups. Axioms 2017, 6, 23.

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