In this paper, the Urysohn and completely Hausdorff axioms in general topology are generalized to L-topological spaces so as to be compatible with pointwise metrics. Some properties and characterizations are also derived

In this paper, we introduce the concept of the generalized topological molecular lattices as a generalization of Wang's topological molecular lattices,  topological spaces, fuzzy topological spaces, L-fuzzy topological spaces and soft topological spaces. Topological molecular lattices were defined by closed elements, but in this new structure we present the concept of the open elements and defi...

We study different completeness definitions for two categories of lattice-valued Cauchy spaces and the relations between these definitions. We also show the equivalence of a so-called completion axiom and the existence of a completion.

ur aim of this  paper  is  to introduce the concept of $L$-double fuzzy rough sets in whichboth constructive and axiomatic approaches are used. In constructive approach, a pairof $L$-double fuzzy lower (resp. upper) approximation operators is defined  and the basic properties of them  are studied.From the viewpoint of the axiomatic approach, a set of axioms is constructed to characterize the $L...

In this paper a particular case of z-ideals, called strongly z-ideal, is defined by introducing zero sets in pointfree topology. We study strongly z-ideals, their relation with z-ideals and the role of spatiality in this relation. For strongly z-ideals, we analyze prime ideals using the concept of zero sets. Moreover, it is proven that the intersection of all zero sets of a prime ideal of C(L),...

1 ω Stable/Totally Transcendental Theories Throughout let T be a complete theory in a countable language L having infinite models. For an L-structure M and A ⊆ M let SM n (A) denote the set of n-types of A. We define a topology (called Stone topology) on SM n (A) by setting basic open sets to be of the form Uφ = {p ∈ SM n (A) : φ ∈ p} where φ is an L(A)-formula. Then SM n (A) is totally disconn...

‎It is well known that every (real or complex) normed linear space $L$ is isometrically embeddable into $C(X)$ for some compact Hausdorff space $X$‎. ‎Here $X$ is the closed unit ball of $L^*$ (the set of all continuous scalar-valued linear mappings on $L$) endowed with the weak$^*$ topology‎, ‎which is compact by the Banach--Alaoglu theorem‎. ‎We prove that the compact Hausdorff space $X$ can ...

Introduction and motivation To explain the motivation of our work we give a short glimpse into the history of Fuzzy Topology called more recently Lattice-Valued Topology or Many Valued Topology. In 1968, C. L. Chang [1] introduced the notion of a fuzzy topology on a set X as a subset τ ⊆ [0, 1] satisfying the natural counterparts of the axioms of topology: (1) 0X , 1X ∈ τ ; (2) U, V ∈ τ ⇒ U ∧ V...

We show that the Scott topology induces a topology for real-valued Lipschitz maps on Banach spaces which we call the L-topology. It is the weakest topology with respect to which the L-derivative operator, as a second order functional on the space of Lipschitz maps into the domain of non-empty, convex and weak*-compact valued functions ordered by reverse inclusion, is continuous. For finite dime...