Resumen de Notes on closed mappings

Chuan Liu

• In this paper, we characterize closed sigma-compact images of metric spaces as Fr\'echet, weakly quasi-first-countable spaces with a sigma-locally finite k-network; and discuss the fibers of closed mappings on some generalized metric spaces and improve some Tanaka's results and answered a Yun's question. It is also shown that g-metrizable spaces and spaces with a point-countable base are preserved by closed sequence-covering mappings, which gives an affirmative answer to a Lin's question.