Locally n-Connected Compacta and UVn-Maps
Keyword(s):
A Cell
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Abstract We provide a machinery for transferring some properties of metrizable ANR-spaces to metrizable LCn-spaces. As a result, we show that for completely metrizable spaces the properties ALCn, LCn and WLCn coincide to each other. We also provide the following spectral characterizations of ALCn and celllike compacta: A compactum X is ALCn if and only if X is the limit space of a σ-complete inverse system S = {Xα , pβ α , α < β < τ} consisting of compact metrizable LCn-spaces Xα such that all bonding projections pβα, as a well all limit projections pα, are UVn-maps. A compactum X is a cell-like (resp., UVn) space if and only if X is the limit space of a σ-complete inverse system consisting of cell-like (resp., UVn) metrizable compacta.
2003 ◽
Vol 133
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pp. 89-95
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1993 ◽
Vol 340
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pp. 871-883
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1982 ◽
Vol 84
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pp. 437-437
2014 ◽
Vol 15
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pp. 1-28
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1986 ◽
Vol 96
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pp. 513-513
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2000 ◽
Vol 129
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pp. 1535-1544
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