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pro vyhledávání: '"54A05, 54A20"'
Autor:
Wojciechowski, Jerzy
In this note it is proved that the class of paratopologies is simple and that under the assumption that the measurable cardinals form a proper class, the class of hypotopologies is not simple. Moreover, an example is given of a Hausdorff convergence
Externí odkaz:
http://arxiv.org/abs/2110.03538
Autor:
Brandenburg, Martin
For a (possibly large) realized limit sketch $\mathcal{S}$ such that every $\mathcal{S}$-model is small in a suitable sense we show that the category of cocontinuous functors $\mathsf{Mod}(\mathcal{S}) \to \mathcal{C}$ into a cocomplete category $\ma
Externí odkaz:
http://arxiv.org/abs/2106.11115
Publikováno v:
Topology and its Applications 285 (2020) 107391
This article is a reflection on the mathematical legacy of Professor Petr Simon.
Externí odkaz:
http://arxiv.org/abs/2009.08316
Autor:
Hofmann, Dirk, Reis, Carla
Generalising Nachbin's theory of "topology and order", in this paper we continue the study of quantale-enriched categories equipped with a compact Hausdorff topology. We compare these $\mathcal{V}$-categorical compact Hausdorff spaces with ultrafilte
Externí odkaz:
http://arxiv.org/abs/1705.08671
Autor:
Mynard, Frédéric, Trott, William
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 of maps (types of quotient maps, closed maps, and variants of perfect
Externí odkaz:
http://arxiv.org/abs/1411.0633
Autor:
Hofmann, Dirk
Employing a formal analogy between ordered sets and topological spaces, over the past years we have investigated a notion of cocompleteness for topological, approach and other kind of spaces. In this new context, the down-set monad becomes the filter
Externí odkaz:
http://arxiv.org/abs/1212.5539
Autor:
Gutierres, Gonçalo, Hofmann, Dirk
In analogy to the situation for continuous lattices which were introduced by Dana Scott as precisely the injective T$_0$ spaces via the (nowadays called) Scott topology, we study those metric spaces which correspond to injective T$_0$ approach spaces
Externí odkaz:
http://arxiv.org/abs/1103.4744
Autor:
Hofmann, Dirk
The main source of inspiration for the present paper is the work of R. Rosebrugh and R.J. Wood on constructive complete distributive lattices where the authors employ elegantly the concepts of adjunction and module in their study of ordered sets. Bot
Externí odkaz:
http://arxiv.org/abs/1009.3892
Autor:
Dontchev, Julian
In 1990, Ganster and Reilly proved that a function is continuous if and only if it is precontinuous and LC-continuous. In this paper we extend their decomposition of continuity in terms of ideals. We show that a function $f \colon (X,\tau,{\cal I}) \
Externí odkaz:
http://arxiv.org/abs/math/9901017
Autor:
Frédéric Mynard, William Trott
Publikováno v:
Topology and its Applications. 200:251-267
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 of maps (types of quotient maps, closed maps, and variants of perfect
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::943ec2f966e859cfc9e28e01cc43921d
https://doi.org/10.1016/j.topol.2015.06.013
https://doi.org/10.1016/j.topol.2015.06.013
