Free topological inverse semigroups as infinite-dimensional manifolds

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dc.creatorBanakh, T.
dc.creatorHryniv, O.
dc.date2008-10-16
dc.date.accessioned2026-07-07T10:10:53Z
dc.date.available2026-07-07T10:10:53Z
dc.descriptionLet $K$ be a complete quasivariety of topological inverse Clifford semigroups, containing all topological semilattices. It is shown that the free topological inverse semigroup $F(X,K)$ of $X$ in the class $K$ is an $R^\infty$-manifold if and only if $X$ has no isolated points and $F(X,K)$ is a retract of an $R^\infty$-manifold. We derive from this that for any retract $X$ of an $R^\infty$-manifold the free topological inverse semigroup $F(X,K)$ is an $R^\infty$-manifold if and only if the space $X$ has no isolated points. Also we show that for any homotopically equivalent retracts $X,Y$ of $R^\infty$-manifolds with no isolated points the free topological inverse semigroups $F(X,K)$ and $F(Y,K)$ are homeomorphic. This allows us to construct non-homeomorphic spaces whose free topological inverse semigroups are homeomorphic.
dc.description8 pages
dc.identifierhttps://arxiv.org/abs/0810.3026
dc.identifierhttp://arxiv.org/abs/0810.3026
dc.identifierAlgebraical Structures and their Applications, Kyiv: Inst. Mat. NANU, (2002) 132-139
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/171724
dc.subjectGeneral Topology
dc.subject22A15; 20M18; 57N20
dc.titleFree topological inverse semigroups as infinite-dimensional manifolds
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