Geodesic
On classification of spaces of continuous $S^1$-valued functions on polihydrons
Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 4 (2015), pp. 15-20

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In this paper, the spaces of continuous $S^1$-valued functions $C_p(X,S^1)$ are considered. It is proved that if $X$ is a $n$-dimensional polihydron and $S^1$ is a circle which is considered as a topological group, then the topological group $C_p(X,S^1)$ is topologically isomorphic to $C_p(\Delta_n,S^1)$, where $\Delta_n$ is an $n$-dimensional simplex, $n\geqslant1$.
Keywords: almost ring, topological almost module, continuous homomorphism, space of continuous functions
Mots-clés : polihydron, isomorphism. 
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     author = {S. P. Gulko and A. V. Titova},
     title = {On classification of spaces of continuous $S^1$-valued functions on polihydrons},
     journal = {Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika},
     pages = {15--20},
     publisher = {mathdoc},
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     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VTGU_2015_4_a1/}
}
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S. P. Gulko; A. V. Titova. On classification of spaces of continuous $S^1$-valued functions on polihydrons. Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 4 (2015), pp. 15-20. http://geodesic.mathdoc.fr/item/VTGU_2015_4_a1/