On filling an irreducible continuum with the Cartesian product of an arc with a simple triod
On filling an irreducible continuum with the Cartesian product of 1-dimensional continua
On finite powers of countably compact groups
We will show that under for each there exists a group whose -th power is countably compact but whose -th power is not countably compact. In particular, for each there exists and a group whose -th power is countably compact but the -st power is not countably compact.
On Frolík’s characterization of class
On function spaces of compact subspaces of Σ-products of the real line
On inhomogeneity of products of compact F-spaces
On lexicographic products
On locales whose countably compact sublocales have compact closure
Among completely regular locales, we characterize those that have the feature described in the title. They are, of course, localic analogues of what are called -isocompact spaces. They have been considered in T. Dube, I. Naidoo, C. N. Ncube (2014), so here we give new characterizations that do not appear in this reference.
On maps preserving connectedness and/or compactness
We call a function P-preserving if, for every subspace with property P, its image also has property P. Of course, all continuous maps are both compactness- and connectedness-preserving and the natural question about when the converse of this holds, i.e. under what conditions such a map is continuous, has a long history. Our main result is that any nontrivial product function, i.e. one having at least two nonconstant factors, that has connected domain, range, and is connectedness-preserving...
On metric products
On metrization of the uniformity of a product of metric spaces
On Michael's problem concerning the Lindelöf property in the Cartesian products
On movability and other similar shape properties
On multisequences and their application to products of sequential spaces
On N. Noble's theorems concerning powers of spaces and mappings
On -thin dense sets in powers of topological spaces
A subset of a product of topological spaces is called -thin if every its two distinct points differ in at least coordinates. We generalize a construction of Gruenhage, Natkaniec, and Piotrowski, and obtain, under CH, a countable space without isolated points such that contains an -thin dense subset, but does not contain any -thin dense subset. We also observe that part of the construction can be carried out under MA.
On powers of Lindelöf spaces
We present a forcing construction of a Hausdorff zero-dimensional Lindelöf space whose square is again Lindelöf but its cube has a closed discrete subspace of size , hence the Lindelöf degree . In our model the Continuum Hypothesis holds true. After that we give a description of a forcing notion to get a space such that for all positive integers , but .
On Preservation Of Normality.
On products of incompressible AR's
On products of pseudoradial ѕpaces