Geodesic
On the dimension theory of metrizable spaces with periodic homeo­mor­phisms
Sbornik. Mathematics, Tome 27 (1975) no. 1, pp. 67-76
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For every metric space $X$ with homeomorphism $a\colon X\to X$ of prime period $p$ ($a^p=e_X$) we construct a zero-dimensional metric space $P$ ($\dim P=0$) with homeomorphism $b\colon P\to P$ of the same period $p$, together with a closed mapping $f\colon P\to X$ onto $X$, commuting with $a$ and $b$, such that $\operatorname{Ord}f\leqslant \dim X+1$ if $X$ is finite-dimensional and $\operatorname{Ord}f<\infty$ if $X$ is countable-dimensional. Bibliography: 12 titles. 
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S. A. Bogatyi; M. Madirimov. On the dimension theory of metrizable spaces with periodic homeo­mor­phisms. Sbornik. Mathematics, Tome 27 (1975) no. 1, pp. 67-76. http://geodesic.mathdoc.fr/item/SM_1975_27_1_a4/

[1] P. S. Aleksandrov, B. A. Pasynkov, Vvedenie v teoriyu razmernosti Moskva, izd-vo «Nauka», Moskva, 1973 | MR

[2] A. M. Gleason, “Spaces with a compact Lie group of transformations”, Proc. Amer. Math. Soc., 1 (1950), 35–43 | DOI | MR | Zbl

[3] J. W. Jaworowski, “Extensions of maps in spaces with periodic homeomorphisms”, Bull. Amer. Math. Soc., 78:4 (1972), 527–531 | DOI | MR | Zbl

[4] J. W. Jaworowski, “Equivariant extensions of maps”, Pacific J. Math., 45:1 (1973), 229–244 | MR | Zbl

[5] M. Katetov, “O razmernosti metricheskikh prostranstv”, DAN SSSR, 79:2 (1951), 189–191 | MR | Zbl

[6] M. Katetov, “O razmernosti neseparabelnykh prostranstv, I”, Chekhoslov. matem. zh., 2:4 (1952), 333–368 | MR | Zbl

[7] K. Morita, “A condition for the metrizability of topological spaces and for $n$-dimensionality”, Sci. Rep. Tokyo Kyoiku Daigaku, 5 (1955), 33–36 | MR | Zbl

[8] K. Morita, “Normal families and dimension theory in metric spaces”, Math. Ann., 128:4 (1954), 350–362 | DOI | MR | Zbl

[9] K. Nagami, “A note on Hausdorff spaces with the star-finite property. I, II, III”, Proc. Japan Acad., 37 (1961), 131–134 ; 189–192 ; 356–357 | DOI | MR | Zbl | Zbl | MR | Zbl

[10] J. Nagata, Modern dimension theory, Amsterdam, 1965

[11] J. Nagata, “On the countable sum of zero-dimensional metric spaces”, Fundam. Math., 48 (1960), 1–14 | MR | Zbl

[12] R. S. Palais, “The classification of $G$-spaces”, Mem. Amer. Math. Soc., 36, 1960 | MR | Zbl