Shrinking certain sliced decompositions of

Authors:
Robert J. Daverman and D. Kriss Preston

Journal:
Proc. Amer. Math. Soc. **79** (1980), 477-483

MSC:
Primary 54B15; Secondary 54B10

MathSciNet review:
567997

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Abstract: We set forth a connection, based on relatively elementary techniques, between the shrinkability of product decompositions of and that of sliced decompositions. In particular, if *G* is a decomposition of such that each decomposition element *g* is contained in some horizontal slice and if the decomposition of , consisting of those subsets *g* of for which , expands to a shrinkable decomposition of , we show then that *G* itself is shrinkable.

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DOI:
https://doi.org/10.1090/S0002-9939-1980-0567997-8

Keywords:
Upper semicontinuous decomposition,
cell-like,
shrinkable decomposition,
shrinkability criterion,
sliced decomposition,
embedding dimension

Article copyright:
© Copyright 1980
American Mathematical Society