Each topological group embeds into a duoseparable topological group
Autor: | Igor Guran, Alex Ravsky, Taras Banakh |
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Jazyk: | angličtina |
Rok vydání: | 2020 |
Předmět: |
Functor
Unital Existential quantification 010102 general mathematics General Topology (math.GN) Group Theory (math.GR) 01 natural sciences 010101 applied mathematics Combinatorics Identity (mathematics) 22A05 22A22 22B05 54D65 FOS: Mathematics Countable set Geometry and Topology Locally compact space Topological group 0101 mathematics Abelian group Mathematics - Group Theory Mathematics Mathematics - General Topology |
Popis: | A topological group $X$ is called $duoseparable$ if there exists a countable set $S\subseteq X$ such that $SUS=X$ for any neighborhood $U\subseteq X$ of the unit. We construct a functor $F$ assigning to each (abelian) topological group $X$ a duoseparable (abelain-by-cyclic) topological group $FX$, containing an isomorphic copy of $X$. In fact, the functor $F$ is defined on the category of unital topologized magmas. Also we prove that each $\sigma$-compact locally compact abelian topological group embeds into a duoseparable locally compact abelian-by-countable topological group. Comment: 9 pages |
Databáze: | OpenAIRE |
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