Fréchet property in compact spaces is not preserved by -equivalence
An example of two -equivalent (hence -equivalent) compact spaces is presented, one of which is Fréchet and the other is not.
Free non-archimedean topological groups
We study free topological groups defined over uniform spaces in some subclasses of the class of non-archimedean groups. Our descriptions of the corresponding topologies show that for metrizable uniformities the corresponding free balanced, free abelian and free Boolean groups are also metrizable. Graev type ultra-metrics determine the corresponding free topologies. Such results are in a striking contrast with free balanced and free abelian topological groups cases (in standard varieties). Another...