Question

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

Answer 1

here is the definition in words: 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 2

anyone? :(

Answer 3

@satellite73 please help

Answer 4

@Loser66 can you help?

Answer 5

@ganeshie8 please?

Answer 6

\[\exists r>0\ such\ that\ (something \ here?)\]

Answer 7

@zephyr141 ??

Answer 8

what does "logical connectives" mean?

Answer 9

"and","or", "not" you those. And quantifiers.

Answer 10

@myininaya can you help?

Answer 11

\[\exists \epsilon >0\] such that \[N_{\epsilon}(p)=\{q\in X|d(p, q)<\epsilon\}\subset E\]

Answer 12

what is the set?

Answer 13

metric space. and E is in that metric

Answer 14

I give you formal example.
S ={(x,y, z) 0<x<1 , y^2+z^2<=1}
find Int S?
Int S= {(x,y,z)| 0<x<1 , y^2+z^2<1}
If \(p =(x_0,y_0,z_0)\in Int s\)
there exists a ball \(B(p,\varepsilon) \leq Int S\)
for \(\varepsilon =min\{x_0, 1-x_0, 1-\sqrt{y_0^2+z_0^2}\}\)
this set is open.
bd(S) ={(x,y,z) x =0 or x=1 or y^2+z^2 =1}
For any \(p=(x_0,y_0,z_0)\) in this set and \(\forall \varepsilon >0\), B(p,\(\varepsilon\)) contains points in S and points in \(S^c\)
therefore, S\bd S = Int S
and Ext S ={(x,y,z) | s<0 or x >1 or y^2+z^2 >1}

Answer 15

my computer is crazy, it gets many virus; have to log off now.

Answer 16

thank you both :)