Communications of the
Korean Mathematical Society CKMS

We prove that the star operator and the sequential closure operator on a weakly first countable space are the same and show that the Fr\'echetness is a sufficient condition for a weakly first countable space to be first countable.

Keywords: star operator, sequential closure operator, Frechet, first countable, weakly first countable, symmetrizable, semi-metrizable

MSC numbers: 54D80, 54E18, 54E25