Completion functors for Cauchy spaces.
Concerning a certain -algebra in compact Hausdorff spaces
Concerning Sets of the First Baire Category with Respect to Different Metrics
We prove that if and δ are the Hausdorff metric and the radial metric on the space ⁿ of star bodies in ℝ, with 0 in the kernel and with radial function positive and continuous, then a family ⊂ ⁿ that is meager with respect to need not be meager with respect to δ. Further, we show that both the family of fractal star bodies and its complement are dense in ⁿ with respect to δ.
Configurations of points in sets of positive measure and in Baire sets of second category
Convergence of generic infinite products of affine operators.
Convergence results for a class of abstract continuous descent methods.
Criteria of openness for relations
Definably complete Baire structures
We consider definably complete Baire expansions of ordered fields: every definable subset of the domain of the structure has a supremum and the domain cannot be written as the union of a definable increasing family of nowhere dense sets. Every expansion of the real field is definably complete and Baire, and so is every o-minimal expansion of a field. Moreover, unlike the o-minimal case, the structures considered form an axiomatizable class. In this context we prove a version of the Kuratowski-Ulam...
Dense Hyperplanes of First Category.
Dichotomies for and spaces
Jachymski showed that the set is either a meager subset of or is equal to . In the paper we generalize this result by considering more general spaces than , namely , the space of all continuous functions which vanish at infinity, and , the space of all continuous bounded functions. Moreover, we replace the meagerness by -porosity.
Domain representability of
Let be the space of continuous real-valued functions on X, with the topology of pointwise convergence. We consider the following three properties of a space X: (a) is Scott-domain representable; (b) is domain representable; (c) X is discrete. We show that those three properties are mutually equivalent in any normal T₁-space, and that properties (a) and (c) are equivalent in any completely regular pseudo-normal space. For normal spaces, this generalizes the recent result of Tkachuk that is...
Domain-representable spaces
We study domain-representable spaces, i.e., spaces that can be represented as the space of maximal elements of some continuous directed-complete partial order (= domain) with the Scott topology. We show that the Michael and Sorgenfrey lines are of this type, as is any subspace of any space of ordinals. We show that any completely regular space is a closed subset of some domain-representable space, and that if X is domain-representable, then so is any -subspace of X. It follows that any Čech-complete...
Duality of measure and category in infinite-dimensional separable Hilbert space .
Ein Beitrag zur Baire-Kategorie-Theorie.
Epireflections which are completions
Espaces de Baire et espaces de Namioka.
Espaces héréditairement de Baire
Euclidean Convexity Cannot be Compactified.
Expansions of subfields of the real field by a discrete set
Let K be a subfield of the real field, D ⊆ K be a discrete set and f: Dⁿ → K be such that f(Dⁿ) is somewhere dense. Then (K,f) defines ℤ. We present several applications of this result. We show that K expanded by predicates for different cyclic multiplicative subgroups defines ℤ. Moreover, we prove that every definably complete expansion of a subfield of the real field satisfies an analogue of the Baire category theorem.
Extending Stechkin's theorem and beyond.