Question

Real analysis help. What is an interior point of a set written in logical form using logical connectives and quantifiers?


here is the definition in words: Let E be subset of a metric space X. A point p is an interior point of E if there is a neighborhood N of p such that N is subset of E.

Answer 1

@aum can you help?

Answer 2

@iambatman do you know?

Answer 3

@ikram002p please help :D

Answer 4

there exists an r > 0 such that .... It starts out like that

Answer 5

but use connectives and quantifiers instead

Answer 6

Let \( E \in (X,\tau_x)\). A point p is an interior point of E \(\rightarrow\) for \(N\subset E \) \) \(\exists r>0 s.t N<=|r|, \forall P \in N\).

Answer 7

\(\exists p\in E \ \exists \delta > 0 \ (p-\delta,p+\delta)\subset S\subseteq X\)

Answer 8

thank you both :D

Answer 9

oh @zzr0ck3r solution is look more neat xD

Answer 10

i defined a disk and he defined an interval
this is the difference if u wanna know :)

Answer 11

replace S with E.

We could also say \(\exists N(p,\epsilon)\in X \ [N(p,\epsilon)\subseteq E]\)

\(N(x,\epsilon):=\{y\in X \ | \ |x-y|< \epsilon\}\)