in this paper, the concept of countably near ps-compactness inl-topological spaces is introduced, where l is a completely distributive latticewith an order-reversing involution. countably near ps-compactness is definedfor arbitrary l-subsets and some of its fundamental properties are studied.

In this paper, we study some properties of the near SR-compactnessin L-topological spaces, where L is a fuzzy lattice. The near SR-compactness isa kind of compactness between Lowen’s fuzzy compactness and SR-compactness,and it preserves desirable properties of compactness in general topologicalspaces.

We study L-categories of lattice-valued convergence spaces. Suchcategories are obtained by fuzzifying" the axioms of a lattice-valued convergencespace. We give a natural example, study initial constructions andfunction spaces. Further we look into some L-subcategories. Finally we usethis approach to quantify how close certain lattice-valued convergence spacesare to being lattice-valued topologi...

The concepts of semicompactness, countable semicompactness, and the semi-Lindelöf property are introduced in L-topological spaces, where L is a complete de Morgan algebra. They are defined by means of semiopen L-sets and their inequalities. They do not rely on the structure of basis lattice L and no distributivity in L is required. They can also be characterized by semiclosed L-sets and their i...

Our work over the past years shows that not only the collection of (for instance) all topological spaces gives rise to a category, but also each topological space can be seen individually as a category by interpreting the convergence relation x −→ x between ultrafilters and points of a topological space X as arrows in X. Naturally, this point of view opens the door to the use of concepts and id...

In this communication we generalize some recent results of Rump to categories enriched in a commutative quantale V. Using these results, show that every quantale-enriched multicategory admits an injective hull. Finally, expose connection between the Isbell adjunction and construction hulls for topological spaces made by Banaschewski 1973.

We introduce a notion of topological quandle. Given a topological quandle Q we associate to every classical link L in R an invariant JQ(L) which is a topological space (defined up to a homeomorphism). The space JQ(L) can be interpreted as a space of colourings of a diagram of the link L with colours from the quandle Q.

Kochen-Specker theorem rules out the non-contextual assignment of values to physical magnitudes. Here we enrich the usual orthomodular structure of quantum mechanical propositions with modal operators. This enlargement allows to refer consistently to actual and possible properties of the system. By means of a topological argument, more precisely in terms of the existence of sections of sheaves,...

We introduce a new complexity measure of a factorial formal language L: the growth rate of the set of minimal forbidden words. We prove some combinatorial properties of minimal forbidden words. As main result we prove that the growth rate of the set of minimal forbidden words for L is a topological invariant of the dynamical system deened by L.