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BY-NC-ND 3.0 license Open Access Published by De Gruyter Open Access April 29, 2015

Locally n-Connected Compacta and UVn-Maps

  • V. Valov


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 , pβα , 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.


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Received: 2015-1-2
Accepted: 2015-4-10
Published Online: 2015-4-29

© 2015 V. Valov

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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