A NOTE ON WEAKLY FIRST COUNTABLE SPACES

Abstract

We prove that the star operator and the sequential closure operator on a weakly first countable space are the same and show that the Frechetness 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

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References

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Cited by

1. STAR OPERATORS ON sn-NETWORKS vol.27, pp.3, 2012, https://doi.org/10.4134/CKMS.2012.27.3.621
2. The convergence-theoretic approach to weakly first countable spaces and symmetrizable spaces vol.69, pp.1, 2019, https://doi.org/10.1515/ms-2017-0213