On S-closed and Extremally Disconnected Fuzzy Topological Spaces
... Lemma 3.2. Let X be fuzzy almost regular and S-closed. Then X is FED and fuzzy nearly compact (FNC). Proof. Suppose that X is not FED. Then there exists a fuzzy regular open set such that Cl (x) > (x) for some x 2 X and Cl 6= 1X . Let x 2 Cl and x 2= . For every open q-nbd U of x , we ha ...
... Lemma 3.2. Let X be fuzzy almost regular and S-closed. Then X is FED and fuzzy nearly compact (FNC). Proof. Suppose that X is not FED. Then there exists a fuzzy regular open set such that Cl (x) > (x) for some x 2 X and Cl 6= 1X . Let x 2 Cl and x 2= . For every open q-nbd U of x , we ha ...
THE CLOSED-POINT ZARISKI TOPOLOGY FOR
... it is easily seen [4, 2.5(i)] that this topology is a refinement of the natural Zariski topology, in which the closed sets all have the form V (I) : = {[N ] ∈ Irr R | I.N = 0} , where I is an ideal of R, and where [N ] denotes the isomorphism class of a simple module N . Our aim is to show that, und ...
... it is easily seen [4, 2.5(i)] that this topology is a refinement of the natural Zariski topology, in which the closed sets all have the form V (I) : = {[N ] ∈ Irr R | I.N = 0} , where I is an ideal of R, and where [N ] denotes the isomorphism class of a simple module N . Our aim is to show that, und ...
On Fuzzy Topological Spaces Involving Boolean Algebraic Structures
... If , be any two members, then . If is a fuzzy topology on X, then the pair (X, ) is called fuzzy topological space (FTS). The members of are called -open sets. A fuzzy set of X is said to be -closed in (X,) if and only if c is -open set in (X,). When = IX , then (X, ...
... If , be any two members, then . If is a fuzzy topology on X, then the pair (X, ) is called fuzzy topological space (FTS). The members of are called -open sets. A fuzzy set of X is said to be -closed in (X,) if and only if c is -open set in (X,). When = IX , then (X, ...
MM Bonsangue 07-10-1996
... Mathematics often emphasizes the formal correspondence between a notation and its meaning. For example, in mathematical logic, we interpret a formal theory on the basis of a more intuitive mathematical domain which properly ts the theory (that is, the interpretation of all theorems must be valid). ...
... Mathematics often emphasizes the formal correspondence between a notation and its meaning. For example, in mathematical logic, we interpret a formal theory on the basis of a more intuitive mathematical domain which properly ts the theory (that is, the interpretation of all theorems must be valid). ...
Algebraic models for rational G
... with the category of Continuous Weyl Toral Modules (CWTMG ), where objects are sheaves of Q modules over a G topological category T CG whose object space consists of the closed subgroups of G. It is believed that an algebraic model for rational G equivariant spectra (for any compact Lie group G) wil ...
... with the category of Continuous Weyl Toral Modules (CWTMG ), where objects are sheaves of Q modules over a G topological category T CG whose object space consists of the closed subgroups of G. It is believed that an algebraic model for rational G equivariant spectra (for any compact Lie group G) wil ...
Covering space
In mathematics, more specifically algebraic topology, a covering map (also covering projection) is a continuous function p from a topological space, C, to a topological space, X, such that each point in X has an open neighbourhood evenly covered by p (as shown in the image); the precise definition is given below. In this case, C is called a covering space and X the base space of the covering projection. The definition implies that every covering map is a local homeomorphism.Covering spaces play an important role in homotopy theory, harmonic analysis, Riemannian geometry and differential topology. In Riemannian geometry for example, ramification is a generalization of the notion of covering maps. Covering spaces are also deeply intertwined with the study of homotopy groups and, in particular, the fundamental group. An important application comes from the result that, if X is a ""sufficiently good"" topological space, there is a bijection between the collection of all isomorphism classes of connected coverings of X and the conjugacy classes of subgroups of the fundamental group of X.