Abstract

In this paper we study the characterizations of compact-covering and 1-sequence-covering (resp. 2-sequence-covering) images of metric spaces and give a positive answer to the following question: How to characterize first countable spaces whose each compact subset is metrizable by certain images of metric spaces?

Keywords: Metrizable spaces; compact-covering maps; 1-sequence-covering maps; $so$-network; $snf$-countable spaces.

MSC: 54C10, 54D70, 54E40, 54E20, 54E99

Pages:  97--107     

Volume  64 ,  Issue  2 ,  2012