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5 Fasciculi Mathematici

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Some properties of rectifiable spaces

Tuyen L. Q., Tuyen O. N.

Fasciculi Mathematici

2018

Nr 60

181--190

In this paper, we give some properties of rectifiable spaces and their relationship with P-space, metrizable space. These results are used to generalize some results in [2], [9] and [12]. Moreover, we give the conditions for a rectifiable space to be second-countable.

Cauchy symmetric spaces with point-countable cs-networks

Tuyen L. Q.

Fasciculi Mathematici

2016

Nr 57

163--170

In this paper, we prove that a Cauchy symmetric space has a point-countable cs-network if and only if it is a 1-sequence-covering compact-covering quotient π, s-image of a metric space; if and only if it is a sequence-covering quotient π, s-image of a metric space.

A partial answer to a question of Y. Tanaka and Y. Ge

Tuyen L. Q.

Fasciculi Mathematici

2016

Nr 57

157--162

In this paper, we give a partial answer to the problem posed by Y. Tanaka and Y. Ge in [9].

Mapping theorems on spaces with sn-network g-functions

Tuyen L. Q.

Fasciculi Mathematici

2015

Nr 55

199--208

Let Δ be the sets of all topological spaces satisfying the following conditions. (1) Each compact subset of X is metrizable; (2) There exists an sn-network g-function g on X such that if xn → x and yn Є g(n, xn) for all n Є N, then x is a cluster point of {yn}. In this paper, we prove that if X Є Δ, then each sequentially-quotient boundary-compact map on X is pseudo-sequence-covering; if X Є Δ and X has a point-countable sn-network, then each sequence-covering boundary-compact map on X is 1-sequence-covering. As the applications, we give that each sequentially-quotient boundary-compact map on g-metrizable spaces is pseudo-sequence-covering, and each sequence-covering boundary-compact on g-metrizable spaces is 1-sequence-covering.

Remarks on sequence-convering closed maps

Tuyen L. Q.

Fasciculi Mathematici

2014

Nr 53

161--165

In this paper, we prove that each sequence-covering closed map on spaces with point-countable weak bases is 1-sequence-covering (or weak-open).