A property of the Sorgenfrey line
A quasitopos containing CONV and MET as full subcategories.
A Ramsey theorem for polyadic spaces
A polyadic space is a Hausdorff continuous image of some power of the one-point compactification of a discrete space. We prove a Ramsey-like property for polyadic spaces which for Boolean spaces can be stated as follows: every uncountable clopen collection contains an uncountable subcollection which is either linked or disjoint. One corollary is that is not a universal preimage for uniform Eberlein compact spaces of weight at most κ, thus answering a question of Y. Benyamini, M. Rudin and M. Wage....
A remark on monoidal closed structures on top
A remark on the tightness of products
We observe the existence of a -compact, separable topological group and a countable topological group such that the tightness of is countable, but the tightness of is equal to .
A remark on -regular spaces.
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 spectral characterization of skeletal maps
We prove that a map between two realcompact spaces is skeletal if and only if it is homeomorphic to the limit map of a skeletal morphism between ω-spectra with surjective limit projections.
A sum theorem for A-weakly infinite-dimensional spaces
A theorem on expansions into inverse systems of metric spaces
A Theorem On Spaces 2X With The Compact-Open Topology
A theorem on spaces 2x with the compact-open topology.
A three-dimensional spheroidal space which is not a sphere
A topological property of beta(N).
A unique factorization theorem for countable products of circles
About -covers and -networks on the Vietoris hyperspace
We study some generalized metric properties on the hyperspace of finite subsets of a space endowed with the Vietoris topology. We prove that has a point-star network consisting of (countable) -covers if and only if so does . Moreover, has a sequence of -covers with property which is a point-star network if and only if so does , where is one of the following properties: point-finite, point-countable, compact-finite, compact-countable, locally finite, locally countable. On the other...
Absolute countable compactness of products and topological groups
In this paper, we generalize Vaughan's and Bonanzinga's results on absolute countable compactness of product spaces and give an example of a separable, countably compact, topological group which is not absolutely countably compact. The example answers questions of Matveev [8, Question 1] and Vaughan [9, Question (1)].
Absolute n-fold hyperspace suspensions
The notion of an absolute n-fold hyperspace suspension is introduced. It is proved that these hyperspaces are unicoherent Peano continua and are dimensionally homogeneous. It is shown that the 2-sphere is the only finite-dimensional absolute 1-fold hyperspace suspension. Furthermore, it is shown that there are only two possible finite-dimensional absolute n-fold hyperspace suspensions for each n ≥ 3 and none when n = 2. Finally, it is shown that infinite-dimensional absolute n-fold hyperspace suspensions...
Absolutely closed spaces and categories of algebras
Addendum to completion and closure