IOSR Journal of Mathematics (IOSR-JM)
... The identity map f: (X, , I) (Y, ) is Irwg-continuous but not *- continuous. Theorem 3.5: Every continuous function is Irwg-continuous. Proof: Let f be a continuous function and V be a closed set in (Y, ) .Then f-1(V) is closed in (X, , I).Since every closed set is * -closed and hence Irwg – closed, ...
... The identity map f: (X, , I) (Y, ) is Irwg-continuous but not *- continuous. Theorem 3.5: Every continuous function is Irwg-continuous. Proof: Let f be a continuous function and V be a closed set in (Y, ) .Then f-1(V) is closed in (X, , I).Since every closed set is * -closed and hence Irwg – closed, ...
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... Whereas group representations of quantum unitary operators are extensively employed in standard quantum mechanics, the applications of groupoid representations are still under development. For example, a description of stochastic quantum mechanics in curved spacetime (Drechsler and Tuckey, 1996) inv ...
... Whereas group representations of quantum unitary operators are extensively employed in standard quantum mechanics, the applications of groupoid representations are still under development. For example, a description of stochastic quantum mechanics in curved spacetime (Drechsler and Tuckey, 1996) inv ...
Recombination Spaces, Metrics, and Pretopologies
... trivial discrete topology. On the other hand, there is a natural metric associated with every undirected graph Γ(V, E) with vertex set V and edge set E. The canonical distance dΓ (x, y) is defined as the minimum number of edges in any path that connects x with y. There is one-toone correspondence be ...
... trivial discrete topology. On the other hand, there is a natural metric associated with every undirected graph Γ(V, E) with vertex set V and edge set E. The canonical distance dΓ (x, y) is defined as the minimum number of edges in any path that connects x with y. There is one-toone correspondence be ...
Completely N-continuous Multifunctions
... Y and G : Y → Z be multifunctions. If F : X → Y is upper (lower) completely N-continuous and G : Y → Z is upper (lower) semi continuous, then G ◦ F : X → Z is an upper (lower) completely N-continuous multifunction. Proof. Let V ⊆ Z be any open set. From the definition of G ◦ F , we have (G ◦ F )+ (V ...
... Y and G : Y → Z be multifunctions. If F : X → Y is upper (lower) completely N-continuous and G : Y → Z is upper (lower) semi continuous, then G ◦ F : X → Z is an upper (lower) completely N-continuous multifunction. Proof. Let V ⊆ Z be any open set. From the definition of G ◦ F , we have (G ◦ F )+ (V ...
