A quantitative refinement of the closed graph theorem
A quasitopos containing CONV and MET as full subcategories.
A quest for nice kernels of neighbourhood assignments
Given a topological property (or a class) , the class dual to (with respect to neighbourhood assignments) consists of spaces such that for any neighbourhood assignment there is with and . The spaces from are called dually . We continue the study of this duality which constitutes a development of an idea of E. van Douwen used to define -spaces. We prove a number of results on duals of some general classes of spaces establishing, in particular, that any generalized ordered space...
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 random fixed point theorem for multivalued mappings
A reconstruction theorem for locally moving groups acting on completely metrizable spaces
Let G be a group which acts by homeomorphisms on a metric space X. We say the action of G is locally moving on X if for every open U ⊆ X there is a g ∈ G such that g↾X ≠ Id while g↾(X∖U) = Id. We prove the following theorem: Theorem A. Let X,Y be completely metrizable spaces and let G be a group which acts on X and Y with locally moving actions. If the orbits of the action of G on X are of the second category in X and the orbits of the action of G on Y are of the second category...
A reflexivity criterion for Hilbert C*-modules over commutative C*-algebras.
A Regular Space Without a Uniformly Regular Quasi-Uniformity.
A related fixed point theorem in complete metric spaces.
A related fixed point theorem in two fuzzy metric spaces.
A relatively free topological group that is not varietal free
Answering a 1982 question of Sidney A. Morris, we construct a topological group G and a subspace X such that (i) G is algebraically free over X, (ii) G is relatively free over X, that is, every continuous mapping from X to G extends to a unique continuous endomorphism of G, and (iii) G is not a varietal free topological group on X in any variety of topological groups.
A remark on a theorem of Solecki
S. Solecki proved that if is a system of closed subsets of a complete separable metric space , then each Suslin set which cannot be covered by countably many members of contains a set which cannot be covered by countably many members of . We show that the assumption of separability of cannot be removed from this theorem. On the other hand it can be removed under an extra assumption that the -ideal generated by is locally determined. Using Solecki’s arguments, our result can be used...
A remark on almost continuous multifunctions
A remark on common fixed sets of commuting mappings
A Remark On Filter Regularity
A remark on filter regularity.
A remark on Fox's paper on shape
A remark on monoidal closed structures on top
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 Rhoades fixed point theorem for non-self mappings.