## Metrizability of certain point-countable unions.(English)Zbl 1032.54017

The author considers modifications of certain metrizability theorems for spaces having a point-countable cover by metrizable subspaces which determines the topology of the space. The modifications are obtained by replacing the assumption that the point-countable cover determines the topology with a weaker assumption that the topology is determined by the collection of all the finite unions of the elements of this cover.

### MSC:

 54E35 Metric spaces, metrizability 54B15 Quotient spaces, decompositions in general topology 54D55 Sequential spaces