A Regular Space Without a Uniformly Regular Quasi-Uniformity.
A remark on R. G. Woods' paper "The minimum uniform compactification of a metric space" (Fund. Math. 147 (1995), 39–59)
A question raised in R. G. Woods' paper has a simple solution.
A remark on the weak topology of the Hilbert space
A remark on -regular spaces.
A research on characterizations of semi- spaces.
A semifilter approach to selection principles
In this paper we develop the semifilter approach to the classical Menger and Hurewicz properties and show that the small cardinal is a lower bound of the additivity number of the -ideal generated by Menger subspaces of the Baire space, and under every subset of the real line with the property is Hurewicz, and thus it is consistent with ZFC that the property is preserved by unions of less than subsets of the real line.
A semifilter approach to selection principles II: -covers
Developing the idea of assigning to a large cover of a topological space a corresponding semifilter, we show that every Menger topological space has the property provided , and every space with the property is Hurewicz provided . Combining this with the results proven in cited literature, we settle all questions whether (it is consistent that) the properties and [do not] coincide, where and run over , , , , and .
A sequential analogue of the Grothendieck-Pták topology
A short note on separable frames
Following the introduction of separability in frames ([2]) we investigate further properties of this notion and establish some consequences of the Urysohn metrization theorem for frames that are frame counterparts of corresponding results in spaces. In particular we also show that regular subframes of compact metrizable frames are metrizable.
A short proof of Parovičenko's theorem
A short proof of ß(G.. {1}) = G for non-metrizable compact groups.
A solution to Comfort's question on the countable compactness of powers of a topological group
In 1990, Comfort asked Question 477 in the survey book “Open Problems in Topology”: Is there, for every (not necessarily infinite) cardinal number , a topological group G such that is countably compact for all cardinals γ < α, but is not countably compact? Hart and van Mill showed in 1991 that α = 2 answers this question affirmatively under . Recently, Tomita showed that every finite cardinal answers Comfort’s question in the affirmative, also from . However, the question has remained...
A somewhat surprising subspace of
A strengthening of the Katětov-Tong insertion theorem
Normal spaces are characterized in terms of an insertion type theorem, which implies the Katětov-Tong theorem. The proof actually provides a simple necessary and sufficient condition for the insertion of an ordered pair of lower and upper semicontinuous functions between two comparable real-valued functions. As a consequence of the latter, we obtain a characterization of completely normal spaces by real-valued functions.
A subclass of the class MOBI
A subset theorem in dimension theory
A sufficient condition of full normality
We present a direct constructive proof of full normality for a class of spaces (locales) that includes, among others, all metrizable ones.
A SURVEY OF SEMIGROUPS OF CONTINUOUS SELFMAPS.
A theorem of Stone-Čech type, and a theorem of Tychonoff type, without the axiom of choice; and their realcompact analogues
A theorem on mappings