Geodesic
Universality on spaces continuously containing topological groups
Filomat, Tome 35 (2021) no. 12, p. 4087

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DOI

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 τ? 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 τ for the collection of all topological groups of weight ≤ τ. In the present paper we prove that in the class of all topological spaces of weight ≤ τ, which are continuously containing spaces for a collection of topological groups, there are universal elements
DOI : 10.2298/FIL2112087I
Classification : 54H11, 2A05, 54C25
Keywords: Universal spaces, containing spaces, spaces continuously containing topological groups, saturated class of spaces 
S D Iliadis; Yu V Sadovnichy. Universality on spaces continuously containing topological groups. Filomat, Tome 35 (2021) no. 12, p. 4087 . doi: 10.2298/FIL2112087I
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     author = {S D Iliadis and Yu V Sadovnichy},
     title = {Universality on spaces continuously containing topological groups},
     journal = {Filomat},
     pages = {4087 },
     year = {2021},
     volume = {35},
     number = {12},
     doi = {10.2298/FIL2112087I},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2112087I/}
}
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