The search session has expired. Please query the service again.
The search session has expired. Please query the service again.
The search session has expired. Please query the service again.
The search session has expired. Please query the service again.
The search session has expired. Please query the service again.
The search session has expired. Please query the service again.
We show that if a Hausdorff topological space satisfies one of the following properties:
a) has a countable, discrete dense subset and is hereditarily collectionwise Hausdorff;
b) has a discrete dense subset and admits a countable base;
then the existence of a (continuous) weak selection on implies weak orderability. As a special case of either item a) or b), we obtain the result for every separable metrizable space with a discrete dense subset.
Assuming Martin’s Axiom, we provide an example of two Fréchet-Urysohn -spaces, whose product is a non-Fréchet-Urysohn -space. This gives a consistent negative answer to a question raised by T. Nogura.
A topological space is KC when every compact set is closed and SC when every convergent sequence together with its limit is closed. We present a complete description of KC-closed, SC-closed and SC minimal spaces. We also discuss the behaviour of the finite derived set property in these classes.
An estimate for the Novak number of a hyperspace with the Vietoris topology is given. As a consequence it is shown that this cardinal function can decrease passing from a space to its hyperspace.
We calculate the density of the hyperspace of a metric space, endowed with the Hausdorff or the locally finite topology. To this end, we introduce suitable generalizations of the notions of totally bounded and compact metric space.
Download Results (CSV)