Skew compact semigroups

[EN] Skew compact spaces are the best behaving generalization of compact Hausdorff spaces to non-Hausdorff spaces. They are those (X ; τ ) such that there is another topology τ* on X for which τ V τ* is compact and (X; τ ; τ*) is pairwise Hausdorff; under these conditions, τ uniquely determines τ *, and (X; τ*) is also skew compact. Much of the theory of compact T2 semigroups extends to this wider class. We show: A continuous skew compact semigroup is a semigroup with skew compact topology τ, such that the semigroup operation is continuous τ2→ τ. Each of these contains a unique minimal ideal which is an upper set with respect to the specialization order. A skew compact semigroup which is a continuous semigroup with respect to both topologies is called a de Groot semigroup. Given one of these, we show: It is a compact Hausdorff group if either the operation is cancellative, or there is a unique idempotent and S2 = S. Its topology arises from its subinvariant quasimetrics. Each *-closed ideal ≠ S is contained in a proper open ideal.Kopperman, RD.; Robbie, D. (2003). Skew compact semigroups. Applied General Topology. 4(1):133-142. doi:10.4995/agt.2003.2015.SWORD1331424

Study of Rgmc regulation by iron levels, anemia, inflammation and hypoxia

Mémoire numérisé par la Direction des bibliothèques de l'Université de Montréal

Rings of real-valued functions and the finite subcovering property

Let C be a ring of (not necessarily bounded) real-valued functions with a common domain X such that C includes all the constant functions and if f   and lt; C then | f | ε C

Quasi-pseudo-metrization of topological preordered spaces

We establish that every second countable completely regularly preordered space (E,T,\leq) is quasi-pseudo-metrizable, in the sense that there is a quasi-pseudo-metric p on E for which the pseudo-metric p\veep^-1 induces T and the graph of \leq is exactly the set {(x,y): p(x,y)=0}. In the ordered case it is proved that these spaces can be characterized as being order homeomorphic to subspaces of the ordered Hilbert cube. The connection with quasi-pseudo-metrization results obtained in bitopology is clarified. In particular, strictly quasi-pseudometrizable ordered spaces are characterized as being order homeomorphic to order subspaces of the ordered Hilbert cube.Comment: Latex2e, 20 pages. v2: minor changes in the proof of theorem 2.

Fuzzy quasi-metric spaces

[EN] We generalize the notions of fuzzy metric by Kramosil and Michalek, and by George and Veeramani to the quasi-metric setting.We show that every quasi-metric induces a fuzzy quasi-metric and ,conversely, every fuzzy quasi-metric space generates a quasi-metrizable topology. Other basic properties are discussed.The authors acknowledge the support of Generalitat Valenciana, grant GRUPOS 03/027Gregori, V.; Romaguera, S. (2004). Fuzzy quasi-metric spaces. Applied General Topology. 5(1):129-136. https://doi.org/10.4995/agt.2004.2001SWORD1291365

Fuzzy quasi-metrics for the Sorgenfrey line

[EN] We endow the set of real numbers with a family of fuzzy quasi-metrics, in the sense of George and Veeramani, which are compatible with the Sorgenfrey topology. Although these fuzzy quasi-metrics are not deduced explicitly from a quasi-metric, they possess interesting properties related to completeness. For instance, we prove that they are balanced and complete in the sense of Doitchinov and that only one of them is right K-sequentially complete. We also observe that compatible fuzzy quasi-metrics for the Sorgenfrey line cannot be left (weakly right) K-sequentially complete.1 The first and second authors acknowledge the support of Spanish Ministry of Education and Science under Grant MTM 2009-12872-C02-01.Gregori Gregori, V.; Morillas, S.; Roig, B. (2013). Fuzzy quasi-metrics for the Sorgenfrey line. Fuzzy Sets and Systems. 222:98-107. https://doi.org/10.1016/j.fss.2012.11.001S9810722

Nonstandard and Standard Compactifications of Ordered Topological Spaces

We construct the Nachbin ordered compactification and the ordered realcompactification, a notion defined in the paper, of a given ordered topological space as nonstandard ordered hulls. The maximal ideals in the algebras of the differences of monotone continuous functions are completely described. We give also a characterization of the class of completely regular ordered spaces which are closed subspaces of products of copies of the ordered real line, answering a question of T.H. Choe and Y.H. Hong. The methods used are topological (standard) and nonstandard