An n-dimensional compactum which remains n-dimensional after removing all Cantor n-manifolds
An n-dimensional version of Wage's example
An observation for simple expansions.
An observation on Kannan mappings
In order to observe the condition of Kannan mappings more deeply, we prove a generalization of Kannan’s fixed point theorem.
An observation on Krull and derived dimensions of some topological lattices
Let , be an algebraic lattice. It is well-known that with its topological structure is topologically scattered if and only if is ordered scattered with respect to its algebraic structure. In this note we prove that, if is a distributive algebraic lattice in which every element is the infimum of finitely many primes, then has Krull-dimension if and only if has derived dimension. We also prove the same result for , the set of all prime elements of . Hence the dimensions on the lattice...
An observation on spaces with a zeroset diagonal
We say that a space has the discrete countable chain condition (DCCC for short) if every discrete family of nonempty open subsets of is countable. A space has a zeroset diagonal if there is a continuous mapping with , where . In this paper, we prove that every first countable DCCC space with a zeroset diagonal has cardinality at most .
An open-perfect mapping on a hereditarily disconnected space onto a connected space
An operator equation in a Tychonoff space.
An order on subsets of cone metric spaces and fixed points of set-valued contractions.
An R-stable ANR which is not FR-stable
An Ulam stability result on quasi-b-metric-like spaces
In this paper a class of general type α-admissible contraction mappings on quasi-b-metric-like spaces are defined. Existence and uniqueness of fixed points for this class of mappings is discussed and the results are applied to Ulam stability problems. Various consequences of the main results are obtained and illustrative examples are presented.
An uncountable collection of mutually exclusive planar atriodic tree-like continua with positive span
An up-spectral space need not be -spectral.
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...
Analyse relative
Analysis on topological manifolds
Analytic Baire spaces
We generalize to the non-separable context a theorem of Levi characterizing Baire analytic spaces. This allows us to prove a joint-continuity result for non-separable normed groups, previously known only in the separable context.
Analytic sets with countable sections
Anosov theorem for coincidences on nilmanifolds
Suppose that L, L’ are simply connected nilpotent Lie groups such that the groups and in their lower central series have the same dimension. We show that the Nielsen and Lefschetz coincidence numbers of maps f,g: Γ∖L → Γ’∖L’ between nilmanifolds Γ∖L and Γ’∖L’ can be computed algebraically as follows: L(f,g) = det(G⁎ - F⁎), N(f,g) = |L(f,g)|, where F⁎, G⁎ are the matrices, with respect to any preferred bases on the uniform lattices Γ and Γ’, of the homomorphisms between the Lie algebras , ’ of...