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Neighborhood of a Point

Last updated Nov 1, 2022

# Definition

Let $(X, \tau)$ be a Topological Space

. Then a neighborhood of

x \in X

is any

U \in \tau

Open so that

x \in U

.

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Complement of Support of Measure is Union of all Null Open Sets

Complement of Support of Measure is Union of all Null Open Sets

...X : U \text{ is open}, \mu(U) = 0\}$$ Proof Denote $\mathcal{N}_{x} := \{U \subset X : U \text{ is a neighborhood of }x \in X\}$ . By definition of , we know that $$\text{supp}(\mu) = \{x \in X :......

11/7/2022
Dense

Dense

...The of the of $D$ is empt $\forall x \in X$ , either $x \in D$ or $x$ is a of $D$ $\forall x \in X$ , every $U$ of $x$ is not with $D$ . That is......

11/7/2022
Neighborhood of a Point

Neighborhood of a Point

Definition Let $(X, \tau)$ be a . Then a neighborhoo of $x \in X$ is any $U \in \tau$ so that $x \in U$ ....

11/7/2022

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