Abstract
Recently M.M. Choban et al. introduced spaces with fragmentable open sets and such spaces are denoted by fos-spaces. In this paper the properties of fos-spaces are studied. Among other things we show that a space covered by a locally countable family of closed fos-subspaces is a fos-space. We also prove that every Čech complete fos-space contains a dense completely metrizable space, which improves a result by M.M. Choban et al. Further, it is proved that both continuous closed irreducible mappings and continuous finite-to-one open mappings preserve fos-spaces.
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