Displaying similar documents to “Mapping theorems on ℵ -spaces”

On k -spaces and k R -spaces

Jinjin Li (2005)

Czechoslovak Mathematical Journal

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In this note we study the relation between k R -spaces and k -spaces and prove that a k R -space with a σ -hereditarily closure-preserving k -network consisting of compact subsets is a k -space, and that a k R -space with a point-countable k -network consisting of compact subsets need not be a k -space.

k -systems, k -networks and k -covers

Jinjin Li, Shou Lin (2006)

Czechoslovak Mathematical Journal

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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.

On three equivalences concerning Ponomarev-systems

Ying Ge (2006)

Archivum Mathematicum

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Let { 𝒫 n } be a sequence of covers of a space X such that { s t ( x , 𝒫 n ) } is a network at x in X for each x ∈ X . For each n ∈ ℕ , let 𝒫 n = { P β : β ∈ Λ n } and Λ n be endowed the discrete topology. Put M = { b = ( β n ) ∈ Π n ∈ ℕ Λ n : { P β n } forms a network at some point x b i n X } and f : M ⟶ X by choosing f ( b ) = x b for each b ∈ M . In this paper, we prove that f is a sequentially-quotient (resp. sequence-covering, compact-covering) mapping if and only if each 𝒫 n is a c s * -cover (resp. f c s -cover, c f p -cover) of X . As a consequence of this result, we prove that f is a sequentially-quotient, s -mapping if and...

On weakly monotonically monolithic spaces

Liang-Xue Peng (2010)

Commentationes Mathematicae Universitatis Carolinae

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In this note, we introduce the concept of weakly monotonically monolithic spaces, and show that every weakly monotonically monolithic space is a D -space. Thus most known conclusions on D -spaces can be obtained by this conclusion. As a corollary, we have that if a regular space X is sequential and has a point-countable w c s * -network then X is a D -space.