PROPER ACTIONS ON TOPOLOGICAL GROUPS: APPLICATIONS TO QUOTIENT SPACES

In the first case, it is shown that the characters of the free and the free abelian topological groups on X are both equal to the “small cardinal” d if X is compact and metrizable,

Moreover, unlike in the topological context, quotient maps are productive in the category of all convergence spaces with continuous maps as morphisms.. This property plays a key role

Let X and Y be topological spaces with the same finite num- ber of connected components and S be a discrete space.. Assume, moreover, that neither space has two

Let (X, τ ) be a topological space, and let β denote the collection of all clopen subsets of (X, τ ). Finally we point out that in certain situations, in contrast to continuous

Among the resulting topological spaces we have the so called Davey space, where the only non-trivial open set is, let us say, {a}.. This is an interesting topological space to

Suppose that G is a topological group, and H is a locally com- pact subgroup of G such that the quotient space G/H is metacompact (subpara- compact).. Then the space G is

 Note that a Hausdorff topological space X is locally compact if and only if it is core compact, and that the Scott open filter topology on O X then coincides with C k (X, $)

If P is a theoretical property of groups and subgroups, we show that a locally graded group G satisfies the minimal condition for subgroups not having P if and only if either G is