Some Point Set Properties of Merotopic Spaces and Their Cohomology Groups.
Spaces whose connected expansion preserve connected subsets
Study of -closed sets and the related notions in topological spaces.
Sur les espaces de voisinages localement connexes
The common division topology on
A topological space is totally Brown if for each and every nonempty open subsets of we have . Totally Brown spaces are connected. In this paper we consider a topology on the set of natural numbers. We then present properties of the topological space , some of them involve the closure of a set with respect to this topology, while others describe subsets which are either totally Brown or totally separated. Our theorems generalize results proved by P. Szczuka in 2013, 2014, 2016 and by...
The connectedness of degeneracy loci
The connectedness of symmetric degeneracy loci: odd ranks. Appendix to "The connectedness of degeneracy loci" by L. W. Tu
The (dis)connectedness of products of Hausdorff spaces in the box topology
In this paper the following two propositions are proved: (a) If , , is an infinite system of connected spaces such that infinitely many of them are nondegenerated completely Hausdorff topological spaces then the box product can be decomposed into continuum many disjoint nonempty open subsets, in particular, it is disconnected. (b) If , , is an infinite system of Brown Hausdorff topological spaces then the box product is also Brown Hausdorff, and hence, it is connected. A space is Brown if...
The inverse images of hyperconnected sets
The LCC-topology on the space of continuous functions
The Sorgenfrey line has no connected compactification
There is no universal totally disconnected space
Three countable connected spaces
Totally Brown subsets of the Golomb space and the Kirch space
A topological space is totally Brown if for each and every nonempty open subsets of we have . Totally Brown spaces are connected. In this paper we consider the Golomb topology on the set of natural numbers, as well as the Kirch topology on . Then we examine subsets of these spaces which are totally Brown. Among other results, we characterize the arithmetic progressions which are either totally Brown or totally separated in . We also show that and are aposyndetic. Our results...
Totally discontinuous connectivity functions
Trennung und Zusammenhang.
Two countable, biconnected, not widely connected Hausdorff spaces.
Two countable Hausdorff almost regular spaces every continuous map of which into every Urysohn space is constant.
Two remarks on weaker connected topologies
It is shown that no generalized Luzin space condenses onto the unit interval and that the discrete sum of copies of the Cantor set consistently does not condense onto a connected compact space. This answers two questions from [2].
Ueber eine Aufgabe aus der Geometria situs