g-metrizability and Sω

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...

The Euler-lagrange Pde and Finsler Metrizability

In this paper we investigate the following question: under what conditions can a second-order homogeneous ordinary differential equation (spray) be the geodesic equation of a Finsler space. We show that the EulerLagrange partial differential system on the energy function can be reduced to a first order system on this same function. In this way we are able to give effective necessary and suffici...

f -DIVERGENCES - REPRESENTATION THEOREM AND METRIZABILITY

In this talk we are first going to state the so-called ’Representation Theorem’ which provides the representation of general f -divergences in terms of the class of elementary divergences. Then we consider the risk set of a (simple versus simple) testing problem and its characterization by the above mentioned class. These ingredients enable us to prove a sharpening of the ’Range of Values Theor...