Completion theorem for cohomological dimensions

Olszewski, Wojciech

doi:10.1090/S0002-9939-1995-1307554-X

Completion theorem for cohomological dimensions
HTML articles powered by AMS MathViewer

by Wojciech Olszewski

Proc. Amer. Math. Soc. 123 (1995), 2261-2264

DOI: https://doi.org/10.1090/S0002-9939-1995-1307554-X

PDF | Request permission

Abstract:

We prove that for every separable metrizable space X with ${\dim _G}X \leq n$, there exists a metrizable completion Y of X with ${\dim _G}Y \leq n$ provided that G is either a countable group or a torsion group, and with ${\dim _G}Y \leq n + 1$ if G is an arbitrary group.

References

Jerzy Dydak, Cohomological dimension and metrizable spaces, Trans. Amer. Math. Soc. 337 (1993), no. 1, 219–234. MR 1153013, DOI 10.1090/S0002-9947-1993-1153013-X

Cohomological dimension and metrizable spaces

Yukihiro Kodama, Note on an absolute neighborhood extensor for metric spaces, J. Math. Soc. Japan 8 (1956), 206–215. MR 81456, DOI 10.2969/jmsj/00830206
Leonard R. Rubin and Philip J. Schapiro, Cell-like maps onto noncompact spaces of finite cohomological dimension, Topology Appl. 27 (1987), no. 3, 221–244. MR 918533, DOI 10.1016/0166-8641(87)90088-5
John J. Walsh, Dimension, cohomological dimension, and cell-like mappings, Shape theory and geometric topology (Dubrovnik, 1981) Lecture Notes in Math., vol. 870, Springer, Berlin-New York, 1981, pp. 105–118. MR 643526