Addendum to completion and closure
Addition theorems for dense subspaces
We study topological spaces that can be represented as the union of a finite collection of dense metrizable subspaces. The assumption that the subspaces are dense in the union plays a crucial role below. In particular, Example 3.1 shows that a paracompact space which is the union of two dense metrizable subspaces need not be a -space. However, if a normal space is the union of a finite family of dense subspaces each of which is metrizable by a complete metric, then is also metrizable by...
Affine group acting on hyperspaces of compact convex subsets of ℝⁿ
For every n ≥ 2, let cc(ℝⁿ) denote the hyperspace of all nonempty compact convex subsets of the Euclidean space ℝⁿ endowed with the Hausdorff metric topology. Let cb(ℝⁿ) be the subset of cc(ℝⁿ) consisting of all compact convex bodies. In this paper we discover several fundamental properties of the natural action of the affine group Aff(n) on cb(ℝⁿ). We prove that the space E(n) of all n-dimensional ellipsoids is an Aff(n)-equivariant retract of cb(ℝⁿ). This is applied to show that cb(ℝⁿ) is homeomorphic...
Algebra in the superextensions of twinic groups [Book]
Algebraic representation of continua.
Algebras of real-valued uniform maps
Amorphe Potenzen kompakter Räume.
An answer to a question on hyperspaces
An application of the theory of isosceles (ultrametric) spaces to the Trnková-Vinárek theorem
An approach to a dual of regular closure operators
An elementary proof of Noble's theorem on normality of powers
An example in the theory of approximate systems
An approximate inverse sequence of plane continua is constructed which negatively answers a question of S. Mardeši’c related to approximate and usual inverse systems. The example also shows that an important result of M.G. Charalambous cannot be improved. As an application, it is shown that a procedure of making an approximate inverse sequence commutative (“taming”) is discontinuous.
An existence theorem via an intuitive idea and fixed-point theorems
An extension theorem for sober spaces and the Goldman topology.
An observation for simple expansions.
Analyse de récession et résultats de stabilité d’une convergence variationnelle, application à la théorie de la dualité en programmation mathématique
Soit un espace de Banach de dual topologique . (resp. ) désigne l’ensemble des parties non vides convexes fermées de (resp. -fermées de ) muni de la topologie de la convergence uniforme sur les bornés des fonctions distances. Cette topologie se réduit à celle de la métrique de Hausdorff sur les convexes fermés bornés [16] et admet en général une représentation en terme de cette dernière [11]. De plus, la métrique qui lui est associée s’est révélée très adéquate pour l’étude quantitative...
Analyse de récession et résultats de stabilité d'une convergence variationnelle, application à la théorie de la dualité en programmation mathématique
Let X be a Banach space and X' its continuous dual. C(X) (resp. C(X')) denotes the set of nonempty convex closed subsets of X (resp. ω*-closed subsets of X') endowed with the topology of uniform convergence of distance functions on bounded sets. This topology reduces to the Hausdorff metric topology on the closed and bounded convex sets [16] and in general has a Hausdorff-like presentation [11]. Moreover, this topology is well suited for estimations and constructive approximations [6-9]. We...
Another look at the localic Tychonoff theorem
Applications of a mismatch, theorem to decomposition spaces
Approach merotopological spaces and their completion.