A nonmovable space with movable components

Dydak, J.; Segal, J.; Spież, S.

doi:10.1090/S0002-9939-1988-0934894-2

A nonmovable space with movable components
HTML articles powered by AMS MathViewer

by J. Dydak, J. Segal and S. Spież PDF

Proc. Amer. Math. Soc. 102 (1988), 1081-1087 Request permission

Abstract:

In this paper we construct a nonmovable complete metric space of which every component is movable. This construction is based on P. Roy’s famous example of a complete metric space $X$ which has inductive dimension ind $X = 0$ and covering dimension $\dim X = 1$.

References

K. Borsuk, Theory of shape, Lecture Notes Series, No. 28, Aarhus Universitet, Matematisk Institut, Aarhus, 1971. MR 0293602
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 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

Prabir Roy’s space

as a counterexample in shape theory

Prabir Roy, Failure of equivalence of dimension concepts for metric spaces, Bull. Amer. Math. Soc. 68 (1962), 609–613. MR 142102, DOI 10.1090/S0002-9904-1962-10872-6
Edwin H. Spanier, Algebraic topology, McGraw-Hill Book Co., New York-Toronto, Ont.-London, 1966. MR 0210112
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