11 citations · 45 across the 18 of their papers we have counts for
20 papers
On some convergence approach structures on hyperspaces
M. Ateş, F. Mynard, S. Sağıroğlu
In the context of the category of convergence approach spaces and contractions, we introduce and study approach analogs of the upper and lower Kuratowski convergence…
On (pre-) approach spaces within convergence approach spaces
Frédéric Mynard
The purpose of this note is to illustrate a parallel between (pre)topologies when seen among convergence spaces and (pre)approach spaces when seen among convergence approach spaces…
On connected subsets of a convergence space
Bryan Castro Herrejón, Frédéric Mynard
Though a convergence space is connected if and only if its topological modification is connected, connected subsets differ for the convergence and for its topological modification.…
On points of convergence lattices and sobriety for convergence spaces
F. Mynard
We characterize the convergence spaces such that the space of points of in the category of convergence lattices is . On the way, we study vari…
When is a category of adherence-determined convergences simple?
Frédéric Mynard, Jerzy Wojciechowski
Abstract. We provide a characterization of classes of filters for which the full subcategory of formed…
Comparison of countability conditions within three fundamental classifications of convergences
Frédéric Mynard
The interrelations between various classes of convergence spaces defined by countability conditions are studied. Remarkably, they all find characterizations in the usual space of u…
On (ultra-) completeness numbers and (pseudo-) paving numbers
Frédéric Mynard
We study the completeness and ultracompleteness numbers of a convergence space. In the case of a completely regular topological space, the completeness number is countable if and o…
Convergence without points
Jean Goubault-Larrecq, Frédéric Mynard
We introduce a pointfree theory of convergence on lattices and coframes. A convergence lattice is a lattice with a monotonic map from the lattice of filters on to…
The convergence-theoretic approach to g-first countable and symmetrizable spaces
Fadoua Chigr, Frédéric Mynard
This article fits in the context of the approach to topological problems in terms of the underlying convergence space structures, and serves as yet another illustration of the powe…
Remarks on metrizability of dual groups
Frédéric Mynard, Mikhail Tkachenko
We examine sufficient conditions for the dual of a topological group to be metrizable and locally compact.
Measure of compactness for filters in product spaces: Kuratowski-Mròwka in CAP revisited
Frédéric Mynard, William Trott
The first author introduced a measure of compactness for families of sets, relative to a class of filters, in the context of convergence approach spaces. We characterize a variety…
Function spaces and contractive extensions in Approach Theory: The role of regularity
Eva Colebunders, Frédéric Mynard, Will Trott
Two classical results characterizing regularity of a convergence space in terms of continuous extensions of maps on one hand, and in terms of continuity of limits for the continuou…
Exponential Kleisli monoids as Eilenberg-Moore algebras
Dirk Hofmann, Frédéric Mynard, Gavin J. Seal
Lax monoidal powerset-enriched monads yield a monoidal structure on the category of monoids in the Kleisli category of a monad. Exponentiable objects in this category are identifie…
Core compactness and diagonality in spaces of open sets
Francis Jordan, Frederic Mynard
We investigate when the space of open subsets of a topological space endowed with the Scott topology is core compact. Such conditions turn out to be related to i…
Products of compact filters and applications to classical product theorems
F. Mynard
Two results on product of compact filters are shown to be the common principle behind a surprisingly large number of theorems.
Relations that preserve compact filters
F. Mynard
Many classes of maps are characterized as (possibly multi-valued) maps preserving particular types of compact filters.
Group topologies coarser than the Isbell topology
S. Dolecki, F. Jordan, F. Mynard
The Isbell, compact-open and point-open topologies on the set of continuous real-valued maps can be represented as the dual topologies with respect to some collec…
When is the {I}sbell topology a group topology?
S. Dolecki, F. Mynard
Conditions on a topological space under which the space of continuous real-valued maps with the Isbell topology is a topological group (topological vector…
A unified theory of function spaces and hyperspaces: local properties
S. Dolecki, F. Mynard
Many classically used function space structures (including the topology of pointwise convergence, the compact-open topology, the Isbell topology and the continuous convergence) are…
Compatible relations on filters and stability of local topological properties under supremum and product
Francis Jordan, Frederic Mynard
An abstract scheme using particular types of relations on filters leads to general unifying results on stability under supremum and product of local topological properties. We pres…