Non standard metric products.
Non-abelian group structure on the Urysohn universal space
We prove that there exists a non-abelian group structure on the Urysohn universal metric space. More precisely, we introduce a variant of the Graev metric that enables us to construct a free group with countably many generators equipped with a two-sided invariant metric that is isometric to the rational Urysohn space. We list several related open problems.
Non-normality points and nice spaces
J. Terasawa in " are non-normal for non-discrete spaces " (2007) and the author in “On non-normality points and metrizable crowded spaces” (2007), independently showed for any metrizable crowded space that each point of its Čech–Stone remainder is a non-normality point of . We introduce a new class of spaces, named nice spaces, which contains both of Sorgenfrey line and every metrizable crowded space. We obtain the result above for every nice space.
Normality and paracompactness in subsets of product spaces
Normality and paracompactness of Pixley-Roy hyperspaces
Note on category in Cartesian products of metrizable spaces
Note on decompositions of metrizable spaces I
Note on decompositions of metrizable spaces II
Note on extremal points
Note on metrization of quasi-uniform spaces