IOSR Journal of Mathematics (IOSR-JM)
... Definition 2.1: An ideal I on a nonempty set X is a collection of subset of X which satisfies the following properties: (i) A ∈ I and B ⊆ A implies B ∈ I. (ii) A ∈ I and B ⊆ I implies A ∪ B ∈ I. A topological space X, τ with an ideal I on X is called ideal topological space and is denoted by X, τ, I ...
... Definition 2.1: An ideal I on a nonempty set X is a collection of subset of X which satisfies the following properties: (i) A ∈ I and B ⊆ A implies B ∈ I. (ii) A ∈ I and B ⊆ I implies A ∪ B ∈ I. A topological space X, τ with an ideal I on X is called ideal topological space and is denoted by X, τ, I ...
NU2422512255
... A number of examples and result for such space are given. Perhaps most interesting is a version of the Tychonoff theorem which given necessary and sufficient conditions on L for all collection with given cardinality of compact L- spaces to have compact product. We know Tychonoff Theorem as Arbitrary ...
... A number of examples and result for such space are given. Perhaps most interesting is a version of the Tychonoff theorem which given necessary and sufficient conditions on L for all collection with given cardinality of compact L- spaces to have compact product. We know Tychonoff Theorem as Arbitrary ...
The Laplace Operator
... ∆ as multiplication operators. These operators differ in two aspects. On Rn , ∆ is essentially self adjoint i.e. the closure is self adjoint and is the unique self adjoint extension of ∆. Its spectrum is purely continuous and σ(∆) = [0, ∞). On the other hand, Laplace operator on cube (0, 1)n has dis ...
... ∆ as multiplication operators. These operators differ in two aspects. On Rn , ∆ is essentially self adjoint i.e. the closure is self adjoint and is the unique self adjoint extension of ∆. Its spectrum is purely continuous and σ(∆) = [0, ∞). On the other hand, Laplace operator on cube (0, 1)n has dis ...
COMPACT LIE GROUPS Contents 1. Smooth Manifolds and Maps 1
... manifold to Euclidean space in a way that is amenable to the techniques of multivariable calculus. Of course, merely have a function that maps into Euclidean space is insufficient. We wish to impose additional structure (namely a notion of smoothness or infinite differentiability) on the homeomorphi ...
... manifold to Euclidean space in a way that is amenable to the techniques of multivariable calculus. Of course, merely have a function that maps into Euclidean space is insufficient. We wish to impose additional structure (namely a notion of smoothness or infinite differentiability) on the homeomorphi ...
