General hedgehogs in general topology
Generalizations of Lašnev's theorem
Generalizations of the uniform convergence
Generalized Caristi's fixed point theorems.
Generalized cone metric spaces.
Generalized contractions and common fixed point theorems concerning -distance.
Generalized Helly spaces, continuity of monotone functions, and metrizing maps
Given an ordered metric space (in particular, a Banach lattice) E, the generalized Helly space H(E) is the set of all increasing functions from the interval [0,1] to E considered with the topology of pointwise convergence, and E is said to have property (λ) if each of these functions has only countably many points of discontinuity. The main objective of the paper is to study those ordered metric spaces C(K,E), where K is a compact space, that have property (λ). In doing so, the guiding idea comes...
Generalized midset properties characterize geodesic circles and intervals
Generalized projections of Borel and analytic sets
For a σ-ideal I of sets in a Polish space X and for A ⊆ , we consider the generalized projection (A) of A given by (A) = x ∈ X: Ax ∉ I, where =y ∈ X: 〈x,y〉∈ A. We study the behaviour of with respect to Borel and analytic sets in the case when I is a -supported σ-ideal. In particular, we give an alternative proof of the recent result of Kechris showing that [ for a wide class of -supported σ-ideals.
Generalized proximity and uniform spaces. I
Generalized proximity and uniform spaces. II
Generated triangular norms
An overview of generated triangular norms and their applications is presented. Several properties of generated -norms are investigated by means of the corresponding generators, including convergence properties. Some applications are given. An exhaustive list of relevant references is included.
Generation of coreflections in categories
Generic convergence of iterates for a class of nonlinear mappings.
Generic well-posedness in some classes of optimization problems
Geodesics in Asymmetic Metric Spaces
In a recent paper [17] we studied asymmetric metric spaces; in this context we studied the length of paths, introduced the class of run-continuous paths; and noted that there are different definitions of “length spaces” (also known as “path-metric spaces” or “intrinsic spaces”). In this paper we continue the analysis of asymmetric metric spaces.We propose possible definitions of completeness and (local) compactness.We define the geodesics using as admissible paths the class of run-continuous paths.We...
Gluing Hyperconvex Metric Spaces
We investigate how to glue hyperconvex (or injective) metric spaces such that the resulting space remains hyperconvex. We give two new criteria, saying that on the one hand gluing along strongly convex subsets and on the other hand gluing along externally hyperconvex subsets leads to hyperconvex spaces. Furthermore, we show by an example that these two cases where gluing works are opposed and cannot be combined.
Graph topologies and uniform convergence in quasi-uniform spaces.
Gδ -sets in topological spaces and games
Players ONE and TWO play the following game: In the nth inning ONE chooses a set from a prescribed family ℱ of subsets of a space X; TWO responds by choosing an open subset of X. The players must obey the rule that for each n. TWO wins if the intersection of TWO’s sets is equal to the union of ONE’s sets. If ONE has no winning strategy, then each element of ℱ is a -set. To what extent is the converse true? We show that: (A) For ℱ the collection of countable subsets of X: 1. There are subsets...
Hausdorff completions of quasi-uniform spaces