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k -systems, k -networks and k -covers

Jinjin Li, Shou Lin (2006)

Czechoslovak Mathematical Journal

The concepts of k -systems, k -networks and k -covers were defined by A. Arhangel’skiǐ in 1964, P. O’Meara in 1971 and R. McCoy, I. Ntantu in 1985, respectively. In this paper the relationships among k -systems, k -networks and k -covers are further discussed and are established by m k -systems. As applications, some new characterizations of quotients or closed images of locally compact metric spaces are given by means of m k -systems.

Metrization of function spaces with the Fell topology

Hanbiao Yang (2012)

Commentationes Mathematicae Universitatis Carolinae

For a Tychonoff space X , let ↓ C F ( X ) be the family of hypographs of all continuous maps from X to [ 0 , 1 ] endowed with the Fell topology. It is proved that X has a dense separable metrizable locally compact open subset if ↓ C F ( X ) is metrizable. Moreover, for a first-countable space X , ↓ C F ( X ) is metrizable if and only if X itself is a locally compact separable metrizable space. There exists a Tychonoff space X such that ↓ C F ( X ) is metrizable but X is not first-countable.

On confluently graph-like compacta

Lex G. Oversteegen, Janusz R. Prajs (2003)

Fundamenta Mathematicae

For any class 𝒦 of compacta and any compactum X we say that: (a) X is confluently 𝒦-representable if X is homeomorphic to the inverse limit of an inverse sequence of members of 𝒦 with confluent bonding mappings, and (b) X is confluently 𝒦-like provided that X admits, for every ε >0, a confluent ε-mapping onto a member of 𝒦. The symbol 𝕃ℂ stands for the class of all locally connected compacta. It is proved in this paper that for each compactum X and each family 𝒦 of graphs, X is confluently...

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