Document Type
Article
Publication Title
Topology and its Applications
Abstract
Let X and A be compact metric spaces. The main problem studied in this paper is that of finding conditions under which a map f{hook}:A→X can be lifted to a cell-like space; i.e., conditions are sought under which there exist a cell-like continuum Z and continuous maps g:Z→X and f{hook}′:A→Z such that g{ring operator}f{hook}′=f{hook}. A theorem is proved which spells out technical conditions on the embedding of A into X and on the homotopy pro-groups of X under which such a lifting exists. The main corollary asserts the following: If X is UVk+1, dim A≤k, and f{hook}′:A→X is continuous, then there exist a cell-like continuum Z and maps g:Z→X and f{hook}′:A→Z such that g{ring operator}f{hook}′= f{hook}. An example is constructed which shows that the hypothesis cannot be weakened to UVk. The theorem and example are both applied to the problem of calculating UVm groups.
First Page
35
Last Page
46
DOI
10.1016/0166-8641(93)90070-T
Publication Date
3-30-1993
Recommended Citation
Venema, Gerard A., "Cell-like images and UVm groups" (1993). University Faculty Publications and Creative Works. 550.
https://digitalcommons.calvin.edu/calvin_facultypubs/550