#### 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 UV^{m} groups" (1993). *University Faculty Publications*. 550.

https://digitalcommons.calvin.edu/calvin_facultypubs/550