A generalization of the Sierpiński theorem
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- by J. J. Dijkstra PDF
- Proc. Amer. Math. Soc. 91 (1984), 143-146 Request permission
Abstract:
Sierpiński’s theorem admits the following generalization. Let $n$ be a nonnegative integer and $X$ a compact Hausdorff space. If $\left \{ {{F_i}\left | {i \in {\mathbf {N}}} \right .} \right \}$ is a countable closed covering of $X$ such that $\left ( {{F_i} \cap {F_j}} \right ) < n$ for distinct $i$ and $j$ in ${\mathbf {N}}$, then every continuous mapping from ${F_1}$ into the $n$-sphere ${S^n}$ is extendable over $X$.References
- J. J. Dijkstra, Fake topological Hilbert spaces and characterizations of dimension in terms of negligibility, CWI Tract, vol. 2, Stichting Mathematisch Centrum, Centrum voor Wiskunde en Informatica, Amsterdam, 1984. MR 753464
- Ryszard Engelking, Teoria wymiaru, Biblioteka Matematyczna, Tom 51. [Mathematics Library, Vol. 51], Państwowe Wydawnictwo Naukowe, Warsaw, 1977 (Polish). MR 0482696 —, General topology, PWN, Warsaw, 1977. W. Sierpiński, Un théorème sur les continus, Tôhoku Math. J. 13 (1918), 300-303.
Additional Information
- © Copyright 1984 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 91 (1984), 143-146
- MSC: Primary 54F60
- DOI: https://doi.org/10.1090/S0002-9939-1984-0735581-2
- MathSciNet review: 735581