Metrizability vs. Fréchet-Uryshon property

Metrizability and the Frechet-Urysohn Property in Topological Groups

Combinatorial Property Vs Computational Property

A set C can be strongly coded under condition < B, C(A) >, where B and C are classes of sets possibly with other parameters, iff there exists A ∈ B such that every Z ∈ C(A) can be used to compute C. The issue is widely studied especially in effective mathematics and reverse mathematics. In this paper, we focus on three kinds of conditions, namely, density condition, enumeration condition and pa...

Resolvable Maps Preserve Complete Metrizability

Let X be a Polish space, Y a separable metrizable space, and f : X → Y a continuous surjection. We prove that if the image under f of every open set or every closed set is resolvable, then Y is Polish. This generalizes similar results by Sierpiński, Vainštain, and Ostrovsky.

Metrizability of Decomposition Spaces

Remarks on Metrizability

In connection with those paragraphs of my paper Applications of the theory of Boolean rings to general topology (Trans. Amer. Math. Soc. vol. 41 (1937) pp. 375-481) dealing with regular spaces, I have long been curious to know whether certain results proved there could be used to obtain the well known theorem that a separable (Hausdorff) space is metrizable if (and only if) it is regular. Since...