Geodesic
Locallyn-Connected Compacta and UV n-Maps
Analysis and Geometry in Metric Spaces, Tome 3 (2015) no. 1 Cet article a éte moissonné depuis la source The Polish Digital Mathematics Library

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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.
Mots-clés : absolute neighborhood retracts, ALCn-spaces, cell-like maps and spaces, WLCn-spaces, UVn-maps and space 
@article{AGMS_2015_3_1_a1,
     author = {Valov, V.},
     title = {Locallyn-Connected {Compacta} and {UV} {n-Maps}},
     journal = {Analysis and Geometry in Metric Spaces},
     year = {2015},
     volume = {3},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/AGMS_2015_3_1_a1/}
}
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Valov, V. Locallyn-Connected Compacta and UV n-Maps. Analysis and Geometry in Metric Spaces, Tome 3 (2015) no. 1. http://geodesic.mathdoc.fr/item/AGMS_2015_3_1_a1/