𝑁-compactness and shape

Morón, Manuel Alonso

doi:10.1090/S0002-9939-1991-1065953-4

$\textbf {N}$-compactness and shape
HTML articles powered by AMS MathViewer

by Manuel Alonso Morón

Proc. Amer. Math. Soc. 113 (1991), 545-550

DOI: https://doi.org/10.1090/S0002-9939-1991-1065953-4

PDF | Request permission

Abstract:

In this paper we prove that two $\mathbb {N}$-compact spaces are homeomorphic if and only if they have the same shape. We also obtain a result concerning shape domination, and finally we give an answer to the problem of components in shape theory.

References

Karol Borsuk, Theory of shape, Monografie Matematyczne, Tom 59, PWN—Polish Scientific Publishers, Warsaw, 1975. MR 0418088
Jerzy Dydak and Manuel Alonso Morón, Quasicomponents and shape theory, Topology Proc. 13 (1988), no. 1, 73–82. MR 1031970
Jerzy Dydak and Jack Segal, Shape theory, Lecture Notes in Mathematics, vol. 688, Springer, Berlin, 1978. An introduction. MR 520227, DOI 10.1007/BFb0067572
Ryszard Engelking, Topologia ogólna, Biblioteka Matematyczna [Mathematics Library], vol. 47, Państwowe Wydawnictwo Naukowe (PWN), Warsaw, 1975 (Polish). MR 0500779

Dimension theory

Horst Herrlich, ${\mathfrak {E}}$-kompakte Räume, Math. Z. 96 (1967), 228–255 (German). MR 205218, DOI 10.1007/BF01124082
G. Kozlowski and J. Segal, On the shape of $0$-dimensional paracompacta, Fund. Math. 83 (1974), no. 2, 151–154. MR 334142, DOI 10.4064/fm-83-2-151-154
Sibe Mardešić, Shapes for topological spaces, General Topology and Appl. 3 (1973), 265–282. MR 324638, DOI 10.1016/0016-660X(72)90018-9
Sibe Mardešić and Jack Segal, Shape theory, North-Holland Mathematical Library, vol. 26, North-Holland Publishing Co., Amsterdam-New York, 1982. The inverse system approach. MR 676973

On the Wallman-Frink compactification of

-dimensional spaces and shape

S. Mrówka, On universal spaces, Bull. Acad. Polon. Sci. Cl. III. 4 (1956), 479–481. MR 0089401
S. Mrówka, Recent results on $E$-compact spaces, TOPO 72—general topology and its applications (Proc. Second Pittsburgh Internat. Conf., Pittsburgh, Pa., 1972; dedicated to the memory of Johannes H. de Groot), Lecture Notes in Math., Vol. 378, Springer, Berlin, 1974, pp. 298–301. MR 0362231
Stanislaw Mrowka, $N$-compactness, metrizability, and covering dimension, Rings of continuous functions (Cincinnati, Ohio, 1982) Lecture Notes in Pure and Appl. Math., vol. 95, Dekker, New York, 1985, pp. 247–275. MR 789276
R. Engelking and S. Mrówka, On $E$-compact spaces, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astr. Phys. 6 (1958), 429–436. MR 0097042
Peter Nyikos, Prabir Roy’s space $\Delta$ is not $N$-compact, General Topology and Appl. 3 (1973), 197–210. MR 324657, DOI 10.1016/0016-660X(72)90012-8
Prabir Roy, Nonequality of dimensions for metric spaces, Trans. Amer. Math. Soc. 134 (1968), 117–132. MR 227960, DOI 10.1090/S0002-9947-1968-0227960-2

The Stone-Čech compactifications