Metrizability is preserved by closed and sequence-covering maps
by
Shouli Jiang
Department of Mathematics, Shandong University, Jinan 250100, PRC
Coauthors: Pengfei Yan Shou Lin (Ningde Teacher's College, Ningde, Fujian 352100, PRC)

Let f:X --> Y be a map. f is a sequence-covering map if whenever {y_n}_n=1^\infty is a convergent sequence in Y, there is a convergent sequence {x_n}_n=1^\infty in X with each x_n in f^-1(y_n ). f is a 1-sequence-covering map if for each y in Y, there is x in f^-1(y) such that whenever {y_n}_n=1^\infty is a sequence converging to y in Y there is a sequence {x_n}_n=1^\infty converging to x in X with each x_n in f^-1(y_n) . In this paper the structure of closed and sequence-covering maps of metric spaces is investigated, the main results are that if f:X --> Y is a closed and sequence-covering map and X is a metric space, then Y is a metric space and f is a 1-sequence-covering map.

Date received: June 22, 2000