Fuzzy Proper Mapping
... how some of the basic ideas and theorems of point – set topology behave in this generalized setting . Moreover , many properties on a fuzzy topologically space were prove them by Chang 's definition . In this paper we introduce and discuss the concepts of fuzzy proper mapping correspondence from a f ...
... how some of the basic ideas and theorems of point – set topology behave in this generalized setting . Moreover , many properties on a fuzzy topologically space were prove them by Chang 's definition . In this paper we introduce and discuss the concepts of fuzzy proper mapping correspondence from a f ...
Fuzzy Regular Compact Space
... Remark 2.20. Every fuzzy regular open set is a fuzzy open set and every fuzzy regular closed set is a fuzzy closed set . The converse of remark ( 2.20 ) , is not true in general as the following example shows : Example 2.21. Let be a set and be a fuzzy topology on . Notice that is a fuzzy open set i ...
... Remark 2.20. Every fuzzy regular open set is a fuzzy open set and every fuzzy regular closed set is a fuzzy closed set . The converse of remark ( 2.20 ) , is not true in general as the following example shows : Example 2.21. Let be a set and be a fuzzy topology on . Notice that is a fuzzy open set i ...
On Fuzzy γ - Semi Open Sets and Fuzzy γ - Semi
... ) is a fuzzy topological space. The family of all fuzzy closed sets of is c ={0, 1, {a.9, b.3, c.5}, {a.8, b.9, c.8}, {a.9, b.9, c.8}, {a.8, b.3, c.5}}. Let A = {a.4, b.5, c.3} then cl(int(A))= {a.8, b.3, c.5} and int(cl(A))= {a.2, b.7, c.5}.Then int(cl(A))˄ cl(int(A)) = {a.2, b.3, c.5}. By Defi ...
... ) is a fuzzy topological space. The family of all fuzzy closed sets of is c ={0, 1, {a.9, b.3, c.5}, {a.8, b.9, c.8}, {a.9, b.9, c.8}, {a.8, b.3, c.5}}. Let A = {a.4, b.5, c.3} then cl(int(A))= {a.8, b.3, c.5} and int(cl(A))= {a.2, b.7, c.5}.Then int(cl(A))˄ cl(int(A)) = {a.2, b.3, c.5}. By Defi ...
Closed and closed set in supra Topological Spaces
... Definition: 2.2 A Subset A of (X,) is said to be supra S closed in (X,) if Scl (A) Int cl (U) whenever A U and U is supra - open. Definition: 2.3 A Subset A of (X,) is said to be supra closed in (X, ) if Scl (A) Int (U) whenever A U and U is supra - open. Definition: 2.4 A Subs ...
... Definition: 2.2 A Subset A of (X,) is said to be supra S closed in (X,) if Scl (A) Int cl (U) whenever A U and U is supra - open. Definition: 2.3 A Subset A of (X,) is said to be supra closed in (X, ) if Scl (A) Int (U) whenever A U and U is supra - open. Definition: 2.4 A Subs ...
VECTOR-VALUED FUZZY MULTIFUNCTIONS
... (ce(co(f)))(P) includes fu(f(x)+ V). Hence ce(co(f)), is an upper hemicontinuous fuzzy multifunction at x. Definition 5.8: A fuzzy multifunction f:X-+Y from a fuzzy topological space X into a fuzzy topological vector space Y is upper demicontinuous if fU({y E Y: h(y) < a where h is a continuous line ...
... (ce(co(f)))(P) includes fu(f(x)+ V). Hence ce(co(f)), is an upper hemicontinuous fuzzy multifunction at x. Definition 5.8: A fuzzy multifunction f:X-+Y from a fuzzy topological space X into a fuzzy topological vector space Y is upper demicontinuous if fU({y E Y: h(y) < a where h is a continuous line ...
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. ...
Topological Dynamics: Minimality, Entropy and Chaos.
... dynamical system, where X is a (compact) metric (Hausdorff) space with a metric d and f : X → X is a continuous map. A subset M of X is a (topologically) minimal set if M is closed, non-empty and invariant (i.e., f (M) ⊆ M) and if M has no proper subset with these three properties. A dynamical syste ...
... dynamical system, where X is a (compact) metric (Hausdorff) space with a metric d and f : X → X is a continuous map. A subset M of X is a (topologically) minimal set if M is closed, non-empty and invariant (i.e., f (M) ⊆ M) and if M has no proper subset with these three properties. A dynamical syste ...
On Nano Regular Generalized and Nano Generalized
... with respect to R and it is denoted by BR(X). That is BR(X) = UR(X) – LR(X). ...
... with respect to R and it is denoted by BR(X). That is BR(X) = UR(X) – LR(X). ...
General Topology - Fakultät für Mathematik
... 1.3.4 Remark. Analogously to 1.2.5, 1.3.2 can be used to determine the greatest lower bound of a family of topologies on X. In fact, if (Oi )i∈I is a family of toplogies on X then 1.3.2, applied to id: T (X, Oi ) → X shows that the finest topology coarser than all Oi is given by O = i∈I Oi . An impo ...
... 1.3.4 Remark. Analogously to 1.2.5, 1.3.2 can be used to determine the greatest lower bound of a family of topologies on X. In fact, if (Oi )i∈I is a family of toplogies on X then 1.3.2, applied to id: T (X, Oi ) → X shows that the finest topology coarser than all Oi is given by O = i∈I Oi . An impo ...
The Simplicial Lusternik
... The simplicial Lusternik-Schnirelmann category is the definition of LusternikSchnirelmann category for simplicial complexes. The Lusternik-Schnirelmann (LS) category of a topological space X represents the least number n such that there is an open cover of X of n + 1 subsets contractible to a point ...
... The simplicial Lusternik-Schnirelmann category is the definition of LusternikSchnirelmann category for simplicial complexes. The Lusternik-Schnirelmann (LS) category of a topological space X represents the least number n such that there is an open cover of X of n + 1 subsets contractible to a point ...
Metric geometry of locally compact groups
... (fp) finitely presented groups. This will serve as a guideline below, in the more general setting of locally compact groups. Every group Γ has left-invariant metrics which induce the discrete topology, for example that defined by d(γ, γ ′ ) = 1 whenever γ, γ ′ are distinct. The three other classes can ...
... (fp) finitely presented groups. This will serve as a guideline below, in the more general setting of locally compact groups. Every group Γ has left-invariant metrics which induce the discrete topology, for example that defined by d(γ, γ ′ ) = 1 whenever γ, γ ′ are distinct. The three other classes can ...