What Defines a Ball, Interior, and Limit Point in Metric Spaces?

[teme92]

Homework Statement

For a metric space (X,d) and a subset E of X, define each of the terms:

(i) the ball B(p,r), where pεX and r > 0
(ii) p is an interior point of E
(iii) p is a limit point of E

Homework Equations

The Attempt at a Solution

i) B_r(p) = {xεX: d(x.p)≤r}


ii) B_r(p) = {xεX: d(x.p)≥r}

iii) I do not know the answer to this at all.

I do not know if the first two parts are correct either so I would appreciate any help given.

 

[Dick]

Homework Statement

For a metric space (X,d) and a subset E of X, define each of the terms:

(i) the ball B(p,r), where pεX and r > 0
(ii) p is an interior point of E
(iii) p is a limit point of E

Homework Equations

The Attempt at a Solution

i) B_r(p) = {xεX: d(x.p)≤r}


ii) B_r(p) = {xεX: d(x.p)≥r}

iii) I do not know the answer to this at all.

I do not know if the first two parts are correct either so I would appreciate any help given.

i) might be ok, if you mean 'closed ball' and d(x.p) should be d(x,p). But seriously, these are definitions. If you don't know what 'interior' or 'limit point' mean you should look them up. The process of looking them up will give you the definitions.

 

[shortydeb]

https://en.wikipedia.org/wiki/Interior_point

that page has a picture which might help.

 

[teme92]

ok thanks guys for the help :)