DISSERTATIONES MATHEMATICAE Page 1 POLSKA AKADEMIA NAUK, INSTYTUT
MATEMATYCZNY DISSERTATIONES MATHEMATICAE (ROZPRAWY MATEMATYCZNE) …

FREE TOPOLOGICAL GROUPS OF METRIZABLE SPACES Page 1 Mathematics of the
USSR-Izvestiya FREE TOPOLOGICAL GROUPS OF METRIZABLE SPACES To cite this …

Let X be a metrizable space and F (X) and A (X) be the free topological group over X and the
free Abelian topological group over X respectively. We establish the following criteria: 1.(a) …

The topological fundamental group π1top is a homotopy invariant finer than the usual
fundamental group. It assigns to each space a quasitopological group and is discrete on …

Introduction. The purpose of this article is to advertise inverse limits of C-algebras. These are
complete topological*-algebras whose topology is determined by their continuous C …

It is well known that every subgroup of a free group is a free group. However, it is not true in
general that a subgroup of a free topological group is a free topological group. It is shown …

In this paper the free topological vector space V (X) over a Tychonoff space X is defined and
studied. It is proved that V (X) is ak ω-space if and only if X is ak ω-space. If X is infinite, then …

Being motivated by the study of the space C c (X) of all continuous real-valued functions on
a Tychonoff space X with the compact–open topology, we introduced in [16] the concepts of …

We study final group topologies and their relations to compactness properties. In particular,
we are interested in situations where a colimit or direct limit is locally compact, ak ω-space …

In [3], Graev introduced the free product of Hausdorff topological groups G and H (denoted in
this paper by G~ H) and showed it is algebraically the free product G* H and is Hausdorff …