Semitopological properties
Separating sets by Darboux-like functions
We consider the following problem: Characterize the pairs ⟨A,B⟩ of subsets of ℝ which can be separated by a function from a given class, i.e., for which there exists a function f from that class such that f = 0 on A and f = 1 on B (the classical separation property) or f < 0 on A and f > 0 on B (a new separation property).
Sequential completeness of subspaces of products of two cardinals
Let be a cardinal number with the usual order topology. We prove that all subspaces of are weakly sequentially complete and, as a corollary, all subspaces of are sequentially complete. Moreover we show that a subspace of need not be sequentially complete, but note that is sequentially complete whenever and are subspaces of .
Sequential continuity on dyadic compacta and topological groups
We study conditions under which sequentially continuous functions on topological spaces and sequentially continuous homomorphisms of topological groups are continuous.
Sequentially complete spaces
Slightly -continuous functions.
Some generalizations of continuity and quasi-continuity of maps
Some more properties of and regular -closed sets in ideal topological spaces.
Some remarks on almost continuous functions
Some results on (-pre, )-continuous functions.
Some subsets of ideal topological spaces
Some weak forms of continuity in bitopological spaces
Somewhat continuity and some other generalisations of continuity
Somewhat continuous functions
Strong convergence and Dini theorems for non-uniform spaces
Study of -closed sets and the related notions in topological spaces.
Subweakly -continuous functions.
Sums of quasicontinuous functions
It is proved that every real cliquish function defined on a separable metrizable space is the sum of three quasicontinuous functions.
Sur la catégorie des applications quasi-continues
The neighborhood complex of an infinite graph.