A STUDY ON FUZZY LOCALLY δ- CLOSED SETS

... theory [11] and control [12]. The first step of locally closedness was done by Bourbaki [4]. Ganster and Reily used locally closed sets in [7] to define LC-continuity and LC-irresoluteness. The notions of fuzzy -closure derived from regular closed sets and fuzzy -closure of fuzzy sets in a fuzzy top ...

... theory [11] and control [12]. The first step of locally closedness was done by Bourbaki [4]. Ganster and Reily used locally closed sets in [7] to define LC-continuity and LC-irresoluteness. The notions of fuzzy -closure derived from regular closed sets and fuzzy -closure of fuzzy sets in a fuzzy top ...

FUZZY PSEUDOTOPOLOGICAL HYPERGROUPOIDS 1

... As the hyperoperation ”·” is a mapping from H × H to P ∗ (H) giving topologies on H and P ∗ (H) we can speak about the continuity of ”·”. Unfortunately, if a topology is given on H, there is no standard straightforward way of generating a topology on P ∗ (H). This leads to the following definition. ...

... As the hyperoperation ”·” is a mapping from H × H to P ∗ (H) giving topologies on H and P ∗ (H) we can speak about the continuity of ”·”. Unfortunately, if a topology is given on H, there is no standard straightforward way of generating a topology on P ∗ (H). This leads to the following definition. ...

$\ alpha $-compact fuzzy topological spaces

... T h e o r e m 3.6. Let a fuzzy topological space (X,T) be a-compact. Then every family ofT(-closed fuzzy subsets ofX with finite intersection property has non-empty intersection. P r o o f . Let X be a-compact. Let U = {B0i : ft e / } be any family of T r closed fuzzy subsets of X with finite inters ...

... T h e o r e m 3.6. Let a fuzzy topological space (X,T) be a-compact. Then every family ofT(-closed fuzzy subsets ofX with finite intersection property has non-empty intersection. P r o o f . Let X be a-compact. Let U = {B0i : ft e / } be any family of T r closed fuzzy subsets of X with finite inters ...

In mathematics, a manifold is a topological space that resembles Euclidean space near each point. More precisely, each point of an n-dimensional manifold has a neighbourhood that is homeomorphic to the Euclidean space of dimension n. Lines and circles, but not figure eights, are one-dimensional manifolds. Two-dimensional manifolds are also called surfaces. Examples include the plane, the sphere, and the torus, which can all be embedded in three dimensional real space, but also the Klein bottle and real projective plane which cannot.Although a manifold resembles Euclidean space near each point, globally it may not. For example, the surface of the sphere is not a Euclidean space, but in a region it can be charted by means of map projections of the region into the Euclidean plane (in the context of manifolds they are called charts). When a region appears in two neighbouring charts, the two representations do not coincide exactly and a transformation is needed to pass from one to the other, called a transition map.The concept of a manifold is central to many parts of geometry and modern mathematical physics because it allows more complicated structures to be described and understood in terms of the relatively well-understood properties of Euclidean space. Manifolds naturally arise as solution sets of systems of equations and as graphs of functions. Manifolds may have additional features. One important class of manifolds is the class of differentiable manifolds.This differentiable structure allows calculus to be done on manifolds. A Riemannian metric on a manifold allows distances and angles to be measured. Symplectic manifolds serve as the phase spaces in the Hamiltonian formalism of classical mechanics, while four-dimensional Lorentzian manifolds model spacetime in general relativity.