Results 41 to 50 of about 79 (77)

Ascoli-type theorems in the cone metric space setting [PDF]

, 2014
We give some necessary and sufficient conditions for (global) continuity of the limit of a pointwise convergent net of cone metric space-valued functions, defined on a Hausdorff topological space, in terms of weak filter exhaustiveness. In this framework,
Boccuto, A., Dimitriou, X.
core  

A quasitopos containing CONV and MET as full subcategories

International Journal of Mathematics and Mathematical Sciences, Volume 11, Issue 3, Page 417-438, 1988., 1987
We show that convergence spaces with continuous maps and metric spaces with contractions, can be viewed as entities of the same kind. Both can be characterized by a limit function λ which with each filter ℱ associates a map λℱ from the underlying set to the extended positive real line. Continuous maps and contractions can both be characterized as limit
E. Lowen, R. Lowen
wiley   +1 more source

Completion of probabilistic uniform limit spaces [PDF]

, 2004
In this article completions of special probabilistic semiuniform convergence spaces are considered. It turns out that every probabilitic Cauchy space under a given t-norm T (triangular norm) has a completion which, in the special case of probabilistic ...
Nusser, Harald
core  

A maximal chain approach to topology and order

International Journal of Mathematics and Mathematical Sciences, Volume 11, Issue 3, Page 465-472, 1988., 1987
On ordered sets (posets, lattices) we regard topologies (or, more general convergence structures) which on any maximal chain of the ordered set induce its own interval topology. This construction generalizes several well‐known intrinsic structures, and still contains enough to produce interesting results on for instance compactness and connectedness ...
R. Vainio
wiley   +1 more source

Convenient Topology [PDF]

, 1997
. A new viewpoint of Topology, summarized under the name Convenient Topology, is considered in such a way that the structural deficiencies of topological and uniform spaces are remidied. This does not mean that these spaces are superfluous.
Gerhard Preuß
core  

Precompactness And Compactness In The Natural Function Spaces Of The Category Of Semiuniform Convergence Spaces [PDF]

, 1997
. Semiuniform convergence spaces form a common generalization of (symmetric) limit spaces (and thus of symmetric topological spaces) as well as of uniform limit spaces (and thus of uniform spaces) with many convenient properties such as cartesian ...
Gerhard Preu, Gerhard Preuß
core  

Completion Of Semiuniform Convergence Spaces [PDF]

, 1997
. Semiuniform convergence spaces form a common generalization of filter spaces (including symmetric convergence spaces [and thus symmetric topological spaces] as well as Cauchy spaces) and uniform limit spaces (including uniform spaces) with many ...
Gerhard Preuß
core  

Compactness with respect to a convergence structure [PDF]

, 2004
A convergence structure for a category is given by determining convergent nets and their limits for each object of this category under validity of some basic convergence axioms.
Šlapal, Josef
core  

The Topological Universe Of Locally Precompact Semiuniform Convergence Spaces [PDF]

, 1996
. The importance of local precompactness has become apparent in theorems of the Ascoli type proved by Bentley and Herrlich [3] in the realm of filter spaces as well as by Wyler [14] in the realm of uniform limit spaces.
Gerhard Preuß
core  

On SI2-convergence in T0-spaces

Open Mathematics
Recently, Shen et al. showed that the SI2-topology on a T0{T}_{0}-space can be described completely in terms of SI2-convergence, and the SI2-convergence is topological whenever the given space is SI2-continuous.
Yang Yi, Xu Xiaoquan
doaj   +1 more source