Geodesic
Strong shape of the Stone-Čech compactification
Commentationes Mathematicae Universitatis Carolinae, Tome 33 (1992) no. 3, pp. 533-539 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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J. Keesling has shown that for connected spaces $X$ the natural inclusion $e:X\rightarrow \beta X$ of $X$ in its Stone-Čech compactification is a shape equivalence if and only if $X$ is pseudocompact. This paper establishes the analogous result for strong shape. Moreover, pseudocompact spaces are characterized as spaces which admit compact resolutions, which improves a result of I. Lončar.
J. Keesling has shown that for connected spaces $X$ the natural inclusion $e:X\rightarrow \beta X$ of $X$ in its Stone-Čech compactification is a shape equivalence if and only if $X$ is pseudocompact. This paper establishes the analogous result for strong shape. Moreover, pseudocompact spaces are characterized as spaces which admit compact resolutions, which improves a result of I. Lončar.
Classification : 54B35, 54C56, 54D30, 54D35, 55P55
Keywords: inverse system; resolution; Stone-Čech compactification; pseudocompact space; shape; strong shape 
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Mardešić, Sibe. Strong shape of the Stone-Čech compactification. Commentationes Mathematicae Universitatis Carolinae, Tome 33 (1992) no. 3, pp. 533-539. http://geodesic.mathdoc.fr/item/CMUC_1992_33_3_a14/

[1] Dowker C.H.: Mapping theorems for noncompact spaces. Amer. J. Math. 69 (1947), 200-240. | MR

[2] Engelking R.: General Topology. Polish Sci. Publ., Warsaw, 1977. | MR | Zbl

[3] Glicksberg I.: Stone-Čech compactifications of products. Trans. Amer. Math. Soc. 90 (1959), 369-382. | MR | Zbl

[4] Keesling J.: Shape theory and the Stone-Čech compactification. in Proc. Internat. Conference on Geometric Topology, Polish Sci. Publ., Warsaw, 1980, pp. 236-243. | MR | Zbl

[5] Keesling K., Sher R.B.: Shape properties of the Stone-Čech compactification. General Topology and Appl. 9 (1978), 1-8. | MR | Zbl

[6] Lisica Ju.T., Mardešić S.: Coherent prohomotopy and a strong shape category of topological spaces. in Proc. Internat. Topological Conference (Leningrad 1982), Lecture Notes in Math. 1060, Springer-Verlag, Berlin, 1984, pp. 164-173. | MR

[7] Lisica Ju.T., Mardešić S.: Coherent prohomotopy and strong shape theory. Glasnik Mat. 19 (39) (1984), 335-399. | MR

[8] Lončar I.: Some results on resolution of spaces. Rad Jugoslav. Akad. Znan. Umjetn. Matem. Znan. 428 (6) (1987), 37-49. | MR

[9] Mardešić S.: Approximate polyhedra, resolutions of maps and shape fibrations. Fund. Math. 114 (1981), 53-78. | MR

[10] Mardešić S., Segal J.: Shape Theory. North-Holland, Amsterdam, 1982. | MR

[11] Morita K.: On shapes of topological spaces. Fund. Math. 86 (1975), 251-259. | MR | Zbl

[12] Walker R.C.: The Stone-Čech compactification. Springer-Verlag, Berlin, 1974. | MR | Zbl