On inhomogeneity of products of compact F-spaces
On Inverse Limit Of Function Spaces
On lexicographic products
On Limit Permanence of Projectivity and Ingectivity
On linear functorial operators extending pseudometrics
For a functor on the category of metrizable compacta, we introduce a conception of a linear functorial operator extending (for each ) pseudometrics from onto (briefly LFOEP for ). The main result states that the functor of -symmetric power admits a LFOEP if and only if the action of on has a one-point orbit. Since both the hyperspace functor and the probability measure functor contain as a subfunctor, this implies that both and do not admit LFOEP.
On local 1-connectedness of Whitney continua
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 of spaces determined by countable subspaces
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 Mazurkiewicz sets
A Mazurkiewicz set is a subset of a plane with the property that each straight line intersects in exactly two points. We modify the original construction to obtain a Mazurkiewicz set which does not contain vertices of an equilateral triangle or a square. This answers some questions by L.D. Loveland and S.M. Loveland. We also use similar methods to construct a bounded noncompact, nonconnected generalized Mazurkiewicz set.
On metric products
On metrization of hyperspaces
On metrization of the uniformity of a product of metric spaces
On Michael's problem concerning the Lindelöf property in the Cartesian products
On monotonic generalizations of Moore spaces, Čech complete spaces and p-spaces
On movability and other similar shape properties
On multifunctions with closed graphs
The set of points of upper semicontinuity of multi-valued mappings with a closed graph is studied. A topology on the space of multi-valued mappings with a closed graph is introduced.
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.