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On three equivalences concerning Ponomarev-systems

Ying Ge — 2006

Archivum Mathematicum

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 only if it is...

On Ponomarev-Systems

Ying Ge;  Lin Shou — 2007

Bollettino dell'Unione Matematica Italiana

In this paper the relations of mappings and families of subsets are investigated in Ponomarev-systems, and the following results are obtained. (1) f is a sequence-covering (resp. 1-sequence-covering) mapping iff 𝒫 is a csf -network (resp. snf -network) of X for a Ponomarev-system ( f , M , X , 𝒫 ) ; (2) f is a sequence-covering (resp. 1-sequence-covering) mapping iff every 𝒫 n is a cs-cover (resp. wsn-cover) of X for a Ponomarev-system ( f , M , X , { 𝒫 n } ) . As applications of these results, some relations between sequence-covering mappings...

g -metrizable spaces and the images of semi-metric spaces

Ying Ge;  Shou Lin — 2007

Czechoslovak Mathematical Journal

In this paper, we prove that a space X is a g -metrizable space if and only if X is a weak-open, π and σ -image of a semi-metric space, if and only if X is a strong sequence-covering, quotient, π and m s s c -image of a semi-metric space, where “semi-metric” can not be replaced by “metric”.

Spaces with countable s n -networks

Ge Ying — 2004

Commentationes Mathematicae Universitatis Carolinae

In this paper, we prove that a space X is a sequentially-quotient π -image of a metric space if and only if X has a point-star s n -network consisting of c s * -covers. By this result, we prove that a space X is a sequentially-quotient π -image of a separable metric space if and only if X has a countable s n -network, if and only if X is a sequentially-quotient compact image of a separable metric space; this answers a question raised by Shou Lin affirmatively. We also obtain some results on spaces with countable...

A note on monotone countable paracompactness

Ge Ying;  Chris Good — 2001

Commentationes Mathematicae Universitatis Carolinae

We show that a space is MCP (monotone countable paracompact) if and only if it has property ( * ) , introduced by Teng, Xia and Lin. The relationship between MCP and stratifiability is highlighted by a similar characterization of stratifiability. Using this result, we prove that MCP is preserved by both countably biquotient closed and peripherally countably compact closed mappings, from which it follows that both strongly Fréchet spaces and q-space closed images of MCP spaces are MCP. Some results on...

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