In this paper, we proved that a sequential space has a cs＊-regular cs＊-network （or a cs＊-regular weak base） is metrizable, which generalized related results in [6], [12] and [14].
Some topological properties of cone metric spaces are discussed and proved that every cone metric space （X, d） is complete if and only if every family of closed subsets of X which has the finite intersection propert...Some topological properties of cone metric spaces are discussed and proved that every cone metric space （X, d） is complete if and only if every family of closed subsets of X which has the finite intersection property and which for every c ε E, 0 〈〈 c contains a set of diameter less that c has non-empty intersection.展开更多
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
基金Supported by the NNSF of China(10571151,10671173)Supported by the NSF of Fujian Province(2006J0228,2008F5066)
文摘In this paper, we proved that a sequential space has a cs＊-regular cs＊-network （or a cs＊-regular weak base） is metrizable, which generalized related results in [6], [12] and [14].
基金Foundation item： Supported by tile National Natural Science Foundation of China（10971185, 10971186） Supported by the Research Fund for Higher Education of Fujian Province（JK2011031）
文摘Some topological properties of cone metric spaces are discussed and proved that every cone metric space （X, d） is complete if and only if every family of closed subsets of X which has the finite intersection property and which for every c ε E, 0 〈〈 c contains a set of diameter less that c has non-empty intersection.
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Foundation item: Supported by the NSF of Fujian(Z0511033)Supported by the Eduction Committee of Fujian(JB04298)Supported by the Eduction Committee of Henan (2004606018, 200510483002)
文摘In this paper, we prove that a space with a compact Countable weak base if and only if it is a weak open cs-image of a metric space.
