Some characterizations of bitopological connectivity properties
Some counterexamples and properties on generalizations of Lindelöf spaces.
Some examples in the dimension theory of Tychonoff spaces
Some examples of continuous images of Radon-Nikodým compact spaces
We provide a characterization of continuous images of Radon-Nikodým compacta lying in a product of real lines and model on it a method for constructing natural examples of such continuous images.
Some examples related to colorings
We complement the literature by proving that for a fixed-point free map the statements (1) admits a finite functionally closed cover with for all (i.e., a coloring) and (2) is fixed-point free are equivalent. When functionally closed is weakened to closed, we show that normality is sufficient to prove equivalence, and give an example to show it cannot be omitted. We also show that a theorem due to van Mill is sharp: for every we construct a strongly zero-dimensional Tychonov space...
Some m-dimensional compacta admitting a dense set of imbeddings into
Some Remarks On Choice Topology
Some remarks on choice topology.
Some remarks on Radon-Nikodym compact spaces
The class of quasi Radon-Nikodým compact spaces is introduced. We prove that this class is closed under countable products and continuous images. It includes the Radon-Nikodým compact spaces. Adapting Alster's proof we show that every quasi Radon-Nikodým and Corson compact space is Eberlein. This generalizes earlier results by J. Orihuela, W. Schachermayer, M. Valdivia and C. Stegall. Further the class of almost totally disconnected spaces is defined and it is shown that every quasi Radon-Nikodým...
Some set-theoretic constructions in topology
Spaces not distinguishing convergences.
Spaces not distinguishing convergences
In the present paper we introduce a convergence condition and continue the study of “not distinguish” for various kinds of convergence of sequences of real functions on a topological space started in [2] and [3]. We compute cardinal invariants associated with introduced properties of spaces.
Spaces not distinguishing pointwise and -quasinormal convergence
In this paper we extend the notion of quasinormal convergence via ideals and consider the notion of -quasinormal convergence. We then introduce the notion of space as a topological space in which every sequence of continuous real valued functions pointwise converging to , is also -quasinormally convergent to (has a subsequence which is -quasinormally convergent to ) and make certain observations on those spaces.
Spaces which admit negative powers and all roots (Preliminary communication)
Spaces with zero set bases
Spaces in which all prime -ideals of are minimal or maximal
Quasi -spaces are defined to be those Tychonoff spaces such that each prime -ideal of is either minimal or maximal. This article is devoted to a systematic study of these spaces, which are an obvious generalization of -spaces. The compact quasi -spaces are characterized as the compact spaces which are scattered and of Cantor-Bendixson index no greater than 2. A thorough account of locally compact quasi -spaces is given. If is a cozero-complemented space and every nowhere dense zeroset...
Special almost P-spaces
Motivated by some examples, we introduce the concept of special almost P-space and show, using the reflection principle, that for every space of this kind the inequality “" holds.
Special lattices of compactifications
SP-scattered spaces; a new generalization of scattered spaces
The set of isolated points (resp. -points) of a Tychonoff space is denoted by (resp. . Recall that is said to be scattered if whenever . If instead we require only that has nonempty interior whenever , we say that is SP-scattered. Many theorems about scattered spaces hold or have analogs for SP-scattered spaces. For example, the union of a locally finite collection of SP-scattered spaces is SP-scattered. Some known theorems about Lindelöf or paracompact scattered spaces hold also...
Stationary sets, trees and continuums.