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MATHEMATICS
On classification of spaces of continuous $S^1$-valued functions on polihydrons
S. P. Gulko, A. V. Titova Tomsk State University, Tomsk, Russian Federation
Abstract:
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, polihydron, isomorphism.
Received: 12.05.2015
Citation:
S. P. Gulko, A. V. Titova, “On classification of spaces of continuous $S^1$-valued functions on polihydrons”, Vestn. Tomsk. Gos. Univ. Mat. Mekh., 2015, no. 4(36), 15–20
Linking options:
https://www.mathnet.ru/eng/vtgu467 https://www.mathnet.ru/eng/vtgu/y2015/i4/p15
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Abstract page: | 156 | Full-text PDF : | 41 | References: | 38 |
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