In this paper,spaces with a locally countable sn-network are discussed.It is shown that a space with a locally countable sn-network iff it is an snf-countable space with a locally countable k-network.As its applicatio...In this paper,spaces with a locally countable sn-network are discussed.It is shown that a space with a locally countable sn-network iff it is an snf-countable space with a locally countable k-network.As its application,almost-open and closed mappings（or finite-to-one and closed mapping） preserve locally countable sn-networks,and a perfect preimage theorem on spaces with a locally countable sn-network is established.展开更多
In this paper internal characterizations on certain quotient images of locally separable metric spaces are discussed.We obtain some descriptions of quotient s-images,pseudo-open s- images,quotient compact images and c...In this paper internal characterizations on certain quotient images of locally separable metric spaces are discussed.We obtain some descriptions of quotient s-images,pseudo-open s- images,quotient compact images and closed images of locally separable metric spaces,and establish some relations between these and certain quotient images of metric spaces by the local separability of suitable subspaces.展开更多
In this paper, we discuss the countable tightness of products of spaces which are quotient simages of locally separable metric spaces, or k-spaces with a star-countable k-network. The main result is that the following...In this paper, we discuss the countable tightness of products of spaces which are quotient simages of locally separable metric spaces, or k-spaces with a star-countable k-network. The main result is that the following conditions are equivalent： （1） b = ω1; （2） t（Sω×Sω1） 〉 ω; （3） For any pair （X, Y）, which are k-spaces with a point-countable k-network consisting of cosmic subspaces, t（X×Y）≤ω if and only if one of X, Y is first countable or both X, Y are locally cosmic spaces. Many results on the k-space property of products of spaces with certain k-networks could be deduced from the above theorem.展开更多
基金Supported by the NNSF of China(1097118510971186)Supported by NSF of Fujian Province(2008F5066)
文摘In this paper,spaces with a locally countable sn-network are discussed.It is shown that a space with a locally countable sn-network iff it is an snf-countable space with a locally countable k-network.As its application,almost-open and closed mappings（or finite-to-one and closed mapping） preserve locally countable sn-networks,and a perfect preimage theorem on spaces with a locally countable sn-network is established.
基金Supported by the National Natural Science Foundation of China
文摘In this paper internal characterizations on certain quotient images of locally separable metric spaces are discussed.We obtain some descriptions of quotient s-images,pseudo-open s- images,quotient compact images and closed images of locally separable metric spaces,and establish some relations between these and certain quotient images of metric spaces by the local separability of suitable subspaces.
基金Supported by the National Science Foundation of China(No.10271026)
文摘In this paper, we discuss the countable tightness of products of spaces which are quotient simages of locally separable metric spaces, or k-spaces with a star-countable k-network. The main result is that the following conditions are equivalent： （1） b = ω1; （2） t（Sω×Sω1） 〉 ω; （3） For any pair （X, Y）, which are k-spaces with a point-countable k-network consisting of cosmic subspaces, t（X×Y）≤ω if and only if one of X, Y is first countable or both X, Y are locally cosmic spaces. Many results on the k-space property of products of spaces with certain k-networks could be deduced from the above theorem.
