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Connections between connected topological spaces on the set of positive integers

100%

Szczuka P.

Open Mathematics

2013

tom 11

nr 5

876-881

In this paper we introduce a connected topology T on the set ℕ of positive integers whose base consists of all arithmetic progressions connected in Golomb’s topology. It turns out that all arithmetic progressions which are connected in the topology T form a basis for Golomb’s topology. Further we examine connectedness of arithmetic progressions in the division topology T′ on ℕ which was defined by Rizza in 1993. Immediate consequences of these studies are results concerning local connectedness of the topological spaces (ℕ, T) and (ℕ, T′).

Locallyn-Connected Compacta and UV n -Maps

84%

Valov V.

Analysis and Geometry in Metric Spaces

2015

tom 3

nr 1

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.

Ograniczanie wyników

1 Analysis and Geometry in Metric Spaces

1 Open Mathematics

1 Szczuka P.

1 Valov V.

1 2015

1 2013

Wyniki wyszukiwania

Connections between connected topological spaces on the set of positive integers

Locallyn-Connected Compacta and UV n -Maps