Criteria for metrisability

Collins, P. J.; Roscoe, A. W.

doi:10.1090/S0002-9939-1984-0733418-9

Criteria for metrisability
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by P. J. Collins and A. W. Roscoe

Proc. Amer. Math. Soc. 90 (1984), 631-640

DOI: https://doi.org/10.1090/S0002-9939-1984-0733418-9

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Abstract:

A simple condition on the local bases of a first countable space is shown to imply metrisability, and some new and some well-known metrisation theorems are deduced. Weakening the condition gives new classes of spaces distinct from the class of metrisable spaces.

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