On a connectedness property of the complements of zeroneighbourhoods in topological vector spaces
On biconnected sets with dispersion points [Book]
On connectedness of proximity spaces
On connectivity properties of bitopological hyperspaces
On connectivity properties of hyperspaces of spaces
On continuous self-maps and homeomorphisms of the Golomb space
The Golomb space is the set of positive integers endowed with the topology generated by the base consisting of arithmetic progressions with coprime . We prove that the Golomb space has continuum many continuous self-maps, contains a countable disjoint family of infinite closed connected subsets, the set of prime numbers is a dense metrizable subspace of , and each homeomorphism of has the following properties: , , , and for all . Here and denotes the set of prime divisors...
On countable connected Hausdorff spaces in which the intersection of every pair of connected subsets is connected.
On countable locally connected spaces
On D-connected sets in the space
On -sequentially regular spaces
On locally connected plane one-to-one continuous images of [0,∞)
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 products of semi-dynamical systems
On separability in semi-stratifiable spaces
On strongly connected spaces
On the associated locally connected space.
On the connectedness of boundary and complement for domains
This article gives a short and elementary proof of the fact that the connectedness of the boundary of an open domain in ℝⁿ is equivalent to the connectedness of its complement.
On the connectedness of some topological spaces
On the construction of biconnected sets
On the continuity and monotonicity of restrictions of connected functions