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.
@article{bwmeta1.element.doi-10_1515_agms-2015-0006,
author = {V. Valov},
title = {Locallyn-Connected Compacta and UV n -Maps},
journal = {Analysis and Geometry in Metric Spaces},
volume = {3},
year = {2015},
zbl = {1325.54007},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_agms-2015-0006}
}
V. Valov. Locallyn-Connected Compacta and UV n -Maps. Analysis and Geometry in Metric Spaces, Tome 3 (2015) . http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_agms-2015-0006/
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