CE-equivalence, $UV^ k$-equivalence and dimension of compacta
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- by Peter Mrozik
- Proc. Amer. Math. Soc. 111 (1991), 865-867
- DOI: https://doi.org/10.1090/S0002-9939-1991-1057958-4
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Abstract:
It is shown that for each $k > 0$ there exists a finite-dimensional continuum $X$ which is not ${\text {U}}{{\text {V}}^k}$-equivalent, and therefore not CE-equivalent, to any continuum $Y$ such that the dimension of $Y$ is equal to the shape dimension of $X$.References
- R. J. Daverman and G. A. Venema, CE equivalence and shape equivalence of $1$-dimensional compacta, Topology Appl. 26 (1987), no. 2, 131–142. MR 896869, DOI 10.1016/0166-8641(87)90064-2
- Steve Ferry, Shape equivalence does not imply CE equivalence, Proc. Amer. Math. Soc. 80 (1980), no. 1, 154–156. MR 574526, DOI 10.1090/S0002-9939-1980-0574526-1 —, $U{V^k}$-equivalent compacta, Geometric Topology and Shape Theory (S. Mardešić and J. Segal, eds.), Lecture Notes in Math., vol. 1283, Springer-Verlag, Berlin, Heidelberg, and New York, 1987, pp. 88-114.
- 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
- Peter Mrozik, Continua that are shape-equivalent but not $UV^1$-equivalent, Topology Appl. 30 (1988), no. 2, 199–210. MR 967756, DOI 10.1016/0166-8641(88)90018-1
Bibliographic Information
- © Copyright 1991 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 111 (1991), 865-867
- MSC: Primary 55P55
- DOI: https://doi.org/10.1090/S0002-9939-1991-1057958-4
- MathSciNet review: 1057958