On some notions related to compactness for locales
On some problems in
On some properties of Hurewicz, Menger, and Rothberger
On some properties of the metric dimension
On some separation axioms and -closure
On some subspaces of the Helly space
On spaces in which a bound on certain cardinal invariants implies closedness
On spaces in which every denumerable subspaces is discrete
On spaces whose denumerable subspaces are discrete
On spaces whose product with every Lindelöf space is Lindelöf
On spaces with point-countable -systems
This paper deals with the behavior of -spaces, countably bi-quasi--spaces and singly bi-quasi--spaces with point-countable -systems. For example, we show that every -space with a point-countable -system is locally compact paracompact, and every separable singly bi-quasi--space with a point-countable -system has a countable -system. Also, we consider equivalent relations among spaces entried in Table 1 in Michael’s paper [15] when the spaces have point-countable -systems.
On spaces with the property of weak approximation by points
A sufficient condition that the product of two compact spaces has the property of weak approximation by points (briefly WAP) is given. It follows that the product of the unit interval with a compact WAP space is also a WAP space.
On star covering properties related to countable compactness and pseudocompactness
We prove a number of results on star covering properties which may be regarded as either generalizations or specializations of topological properties related to the ones mentioned in the title of the paper. For instance, we give a new, entirely combinatorial proof of the fact that -spaces constructed from infinite almost disjoint families are not star-compact. By going a little further we conclude that if is a star-compact space within a certain class, then is neither first countable nor separable....
On -starcompact spaces.
On -starcompact spaces
A space is -starcompact if for every open cover of there exists a Lindelöf subset of such that We clarify the relations between -starcompact spaces and other related spaces and investigate topological properties of -starcompact spaces. A question of Hiremath is answered.
On -starcompact spaces
A space is -starcompact if for every open cover of there exists a countably compact subset of such that In this paper we investigate the relations between -starcompact spaces and other related spaces, and also study topological properties of -starcompact spaces.
On Stone extensions of homotopic maps
On strict and simple type extensions.
On strongly connected spaces
On strongly measure replete lattices and the general Wallman remainder