Open AccessUniversality on spaces continuously containing topological groups
Author(s) -
S.D. Iliadis,
Yu.V. Sadovnichy
Publication year - 2021
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil2112087i
Subject(s) - mathematics , uncountable set , topological space , countable set , topological group , universality (dynamical systems) , fundamental group , homeomorphism (graph theory) , topology (electrical circuits) , topological ring , group (periodic table) , topological vector space , pure mathematics , discrete mathematics , combinatorics , chemistry , physics , organic chemistry , quantum mechanics
In 1986 V.V. Uspenskij proved that there exists a universal topological group with a countable base and in 1990 put the problem: does there exist a universal topological group of weight an uncountable cardinal ?? This problem is still open. In 2015 we gave the notion of a continuously containing space for a given collection of topological groups and proved that there exists such a space of weight ? for the collection of all topological groups of weight ? ?. In the present paper we prove that in the class of all topological spaces of weight ? ?, which are continuously containing spaces for a collection of topological groups, there are universal elements.