A note on splittable spaces
Tkachuk, Vladimir Vladimirovich
Commentationes Mathematicae Universitatis Carolinae, Tome 33 (1992), p. 551-555 / Harvested from Czech Digital Mathematics Library
Access to full text
Full (PDF)

A space $X$ is splittable over a space $Y$ (or splits over $Y$) if for every $A\subset X$ there exists a continuous map $f:X\rightarrow Y$ with $f^{-1} f A=A$. We prove that any $n$-dimensional polyhedron splits over $\bold R^{2n}$ but not necessarily over $\bold R^{2n-2}$. It is established that if a metrizable compact $X$ splits over $\bold R^n$, then $\dim X\leq n$. An example of $n$-dimensional compact space which does not split over $\bold R^{2n}$ is given.

Publié le : 1992-01-01
Classification:  54A25,  54D99 
@article{118522,
     author = {Vladimir Vladimirovich Tkachuk},
     title = {A note on splittable spaces},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {33},
     year = {1992},
     pages = {551-555},
     zbl = {0769.54004},
     mrnumber = {1209296},
     language = {en},
     url = {http://dml.mathdoc.fr/item/118522}
}

Tkachuk, Vladimir Vladimirovich. A note on splittable spaces. Commentationes Mathematicae Universitatis Carolinae, Tome 33 (1992) pp. 551-555. http://gdmltest.u-ga.fr/item/118522/

Arhangel'Skii A.V. A general concept of splittability of a topological space (in Russian), in: Proceedings of the Fifth Tyraspol Symposium on General Topology and its Applications, Kishinev, Shtiintsa, 1985, 8-10.

Arhangel'Skii A.V.; Shakhmatov D.B. Splittable spaces and questions of functions approximations (in Russian), in: Proceedings of the Fifth Tyraspol Symposium on General Topology and its Applications, Kishinev, Shtiintsa, 1985, 10-11.

Arhangel'Skii A.V.; Shakhmatov D.B. On pointwise approximation of arbitrary functions by countable families of continuous functions (in Russian), Trudy Seminara I.G. Petrovskogo 13 (1988), 206-227. (1988) | MR 0961436

Tkachuk V.V. Approximation of $\bold R^X$ with countable subsets of $C_p(X)$ and calibers of the space $C_p(X)$, Comment. Math. Univ. Carolinae 27 (1986), 267-276. (1986) | MR 0857546

Bregman Yu.H.; Šapirovskii B.E.; Šostak A.P. On partition of topological spaces, Časopis pro pěstování mat. 109 (1984), 27-53. (1984) | MR 0741207

Mazurkiewicz S. Sur les problèmes $\kappa $ et $\lambda $ de Urysohn, Fund. Math. 10 (1927), 311-319. (1927)

Tkachuk V. Remainders over discrete spaces - some applications (in Russian), Vestnik MGU, Mat., Mech., no. 4, 1990, 18-21. | MR 1086601

Malyhin V.I. $\beta N$ is prime, Bull. Acad. Polon. Sci., Ser. Mat. 27 (1979), 295-297. (1979) | MR 0552052 | Zbl 0433.54015

Engelking R. General Topology, PWN, Warszawa, 1977. | MR 0500780 | Zbl 0684.54001

Skljarenko E.G. A theorem on maps, lowering dimension (in Russian), Bull. Acad. Polon. Sci., Ser. Mat. 10 (1962), 429-432. (1962) | MR 0149445