On spaces whose nowhere dense subsets are scattered.
On spaces whose product with every Lindelöf space is Lindelöf
On spaces with binary normal subbase
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 ideal convergence property
Let I ⊆ P(ω) be an ideal. We continue our investigation of the class of spaces with the I-ideal convergence property, denoted (I). We show that if I is an analytic, non-countably generated P-ideal then (I) ⊆ s₀. If in addition I is non-pathological and not isomorphic to , then (I) spaces have measure zero. We also present a characterization of the (I) spaces using clopen covers.
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 span and chainable continua
On span and weakly chainable continua
On special metrics characterizing topological properties
On spirals and fixed point property
We study the famous examples of G. S. Young [7] and R. H. Bing [2]. We generalize and simplify a little their constructions. First we introduce Young spirals which play a basic role in all considerations. We give a construction of a Young spiral which does not have the fixed point property (see Section 5) . Then, using Young spirals, we define two classes of uniquely arcwise connected curves, called Young spaces and Bing spaces. These classes are analogous to the examples mentioned above. The definitions...
On splitting of extensions of rings and topological rings.
On Stability in Impulsive Dynamical Systems
Several results on stability in impulsive dynamical systems are proved. The first main result gives equivalent conditions for stability of a compact set. In particular, a generalization of Ura's theorem to the case of impulsive systems is shown. The second main theorem says that under some additional assumptions every component of a stable set is stable. Also, several examples indicating possible complicated phenomena in impulsive systems are presented.
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 stationary sets for certain generalizations of continuity
On Stone extensions of homotopic maps
On stratifiable fuzzy topological spaces
The aim of the paper is to extend the notion of stratifiability from the category Top of topological spaces to the category CFT of [Chang] fuzzy topological spaces and to develop the corresponding theory.
On strict and simple type extensions.