Compact 𝜎-metric Hausdorff spaces are sequential

Compact $\sigma$-metric Hausdorff spaces are sequential
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by A. J. Ostaszewski PDF

Proc. Amer. Math. Soc. 68 (1978), 339-343 Request permission

It is shown that a locally countably compact, regular ${T_2}$ space which may be covered by a countable number of metrizable subspaces is sequential.

References

Suslin number and cardinality. Characters of points in sequential bicompacta

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The closed image of a metric space can be condensed to a metric space

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