A mapping f: X→Y is called weak sequence-covering if whenever {ya} is a sequence in Y converging to y ∈ Y, there exist a subsequence {ynk} and xk∈f^-1(ynk)(k∈N) ,x∈f^-1 (y) such that xk→x. The main results are: ...A mapping f: X→Y is called weak sequence-covering if whenever {ya} is a sequence in Y converging to y ∈ Y, there exist a subsequence {ynk} and xk∈f^-1(ynk)(k∈N) ,x∈f^-1 (y) such that xk→x. The main results are: (1) Y is a sequential, Frechet, strongly Frechet space iff every weak sepuence-covering mapping onto Y is quotient, pseudo-open, countably bi-quotient respectively, (2) weak sequence-covering mapping preserves cs-network and certain k-(cs-)networks, thus some new mapping theorems on k-(cs-)notworks are proved.展开更多
In this paper, we mainly discuss the images of certain spaces under closed sequencecovering maps. It is showed that the property with a locally countable weak base is preserved by closed sequence-covering maps. And th...In this paper, we mainly discuss the images of certain spaces under closed sequencecovering maps. It is showed that the property with a locally countable weak base is preserved by closed sequence-covering maps. And the following question is discussed： Are the closed sequence-covering images of spaces with a point-countable sn-network sn-first countable？展开更多
In this paper,we discuss the closed finite-to-one mapping theorems on generalized metric spaces and their applications.It is proved that point-G_δ properties,■-snf-countability and csf-countability are invariants an...In this paper,we discuss the closed finite-to-one mapping theorems on generalized metric spaces and their applications.It is proved that point-G_δ properties,■-snf-countability and csf-countability are invariants and inverse invariants under closed finite-to-one mappings.By the relationships between the weak first-countabilities,we obtain the closed finite-to-one mapping theorems of weak quasi-first-countability,quasi-first-countability,snf-countability,gfcountability and sof-countability.Furthermore,these results are applied to the study of symmetric products of topological spaces.展开更多
文摘A mapping f: X→Y is called weak sequence-covering if whenever {ya} is a sequence in Y converging to y ∈ Y, there exist a subsequence {ynk} and xk∈f^-1(ynk)(k∈N) ,x∈f^-1 (y) such that xk→x. The main results are: (1) Y is a sequential, Frechet, strongly Frechet space iff every weak sepuence-covering mapping onto Y is quotient, pseudo-open, countably bi-quotient respectively, (2) weak sequence-covering mapping preserves cs-network and certain k-(cs-)networks, thus some new mapping theorems on k-(cs-)notworks are proved.
基金Supported by National Natural Science Foundation of China (Grant Nos.1120141410971185+2 种基金11171162)the Natural Science Foundation of Fujian Province (Grant No.2012J05013)Training Programme Foundation for Excellent Youth Researching Talents of Fujian’s Universities (Grant No.JA13190)
文摘In this paper, we mainly discuss the images of certain spaces under closed sequencecovering maps. It is showed that the property with a locally countable weak base is preserved by closed sequence-covering maps. And the following question is discussed： Are the closed sequence-covering images of spaces with a point-countable sn-network sn-first countable？
基金Supported by the National Natural Science Foundation of China(11801254,11471153)
文摘In this paper,we discuss the closed finite-to-one mapping theorems on generalized metric spaces and their applications.It is proved that point-G_δ properties,■-snf-countability and csf-countability are invariants and inverse invariants under closed finite-to-one mappings.By the relationships between the weak first-countabilities,we obtain the closed finite-to-one mapping theorems of weak quasi-first-countability,quasi-first-countability,snf-countability,gfcountability and sof-countability.Furthermore,these results are applied to the study of symmetric products of topological spaces.
