A Boolean view of sequential compactness
A category Ψ-density topology
Ψ-density point of a Lebesgue measurable set was introduced by Taylor in [Taylor S.J., On strengthening the Lebesgue Density Theorem, Fund. Math., 1958, 46, 305–315] and [Taylor S.J., An alternative form of Egoroff’s theorem, Fund. Math., 1960, 48, 169–174] as an answer to a problem posed by Ulam. We present a category analogue of the notion and of the Ψ-density topology. We define a category analogue of the Ψ-density point of the set A at a point x as the Ψ-density point at x of the regular open...
A Čech function in ZFC
A nontrivial surjective Čech closure function is constructed in ZFC.
A characterization of fuzzy neighborhood commutative division rings.
A characterization of open mapping in terms of convergent sequences.
A characterization of realcompactness in terms of the topology of pointwise convergence on the function space
A characterization of regular fuzzy spaces
A class of completely regular spaces.
A class of spaces determined by sequences with their cluster points
A Classification Of Topological Spaces. Z-Number Of Spaces
A coarse convergence group need not be precompact
A compact ccc non-separable space from a Hausdorff gap and Martin's Axiom
We answer a question of I. Juhasz by showing that MA CH does not imply that every compact ccc space of countable -character is separable. The space constructed has the additional property that it does not map continuously onto .
A compact Hausdorff topology that is a T₁-complement of itself
Topologies τ₁ and τ₂ on a set X are called T₁-complementary if τ₁ ∩ τ₂ = X∖F: F ⊆ X is finite ∪ ∅ and τ₁∪τ₂ is a subbase for the discrete topology on X. Topological spaces and are called T₁-complementary provided that there exists a bijection f: X → Y such that and are T₁-complementary topologies on X. We provide an example of a compact Hausdorff space of size which is T₁-complementary to itself ( denotes the cardinality of the continuum). We prove that the existence of a compact Hausdorff...
A completion functor for Cauchy groups.
A completion of is a field
We define various ring sequential convergences on and . We describe their properties and properties of their convergence completions. In particular, we define a convergence on by means of a nonprincipal ultrafilter on the positive prime numbers such that the underlying set of the completion is the ultraproduct of the prime finite fields . Further, we show that is sequentially precompact but fails to be strongly sequentially precompact; this solves a problem posed by D. Dikranjan.
A construction of the projective modification for a closure-set of a presheaf
A constructive “Closed subgroup theorem” for localic groups and groupoids
A continuous operator extending fuzzy ultrametrics
We consider the problem of simultaneous extension of fuzzy ultrametrics defined on closed subsets of a complete fuzzy ultrametric space. We construct an extension operator that preserves the operation of pointwise minimum of fuzzy ultrametrics with common domain and an operation which is an analogue of multiplication by a constant defined for fuzzy ultrametrics. We prove that the restriction of the extension operator onto the set of continuous, partial fuzzy ultrametrics is continuous with respect...
A contraction theorem in fuzzy metric spaces.
A convergence on Boolean algebras generalizing the convergence on the Aleksandrov cube
We compare the forcing-related properties of a complete Boolean algebra with the properties of the convergences (the algebraic convergence) and on generalizing the convergence on the Cantor and Aleksandrov cube, respectively. In particular, we show that is a topological convergence iff forcing by does not produce new reals and that is weakly topological if satisfies condition (implied by the -cc). On the other hand, if is a weakly topological convergence, then is a -cc algebra...