Let S and T be subsets of R. Find counter-examples for....

[luckyc1423]

1) Let S and T be subsets of R. Find a counter example for each of the following.

a) If P is the set of all isolated points of S, then P is a closed set
b) If S is closed, then cl (int S) = S
c) if S is open, then int (cl S) = S
d) bd (cl S) = bd S
e) bd (bd S) = bd S
f) bd (S U T) = (bd S) U (bd T)
g) bd ( S (upside down U) T) = (bd S) (upside down U) ( bd T)


2) Prove:

a) S is closed iff S = cl S
b) cl S = S U bd S

 

[stapel]

If you're in a class sufficiently-advanced as to be posing these exercises, then you should be aware that "the upside down thingy" is the "set-intersect" symbol. If you do not know this, then I'm afraid you need much more "hands on" and in-depth assistance than we would be able to provide.

If, on the other hand, you are familiar with these topics, then please reply with definitions for the various abbreviations you used, along with your thoughts and attempts on each of these exercises.

Thank you.

Eliz.

 

[luckyc1423]

Lol, I know what the ubside down U is, I just dont know how to write code in the message board to make the symbol show up as an upside down U

 

[pka]

Lol, I know what the ubside down U is, I just dont know how to write code in the message board to make the symbol show up as an upside down U

Tell us what it is and how to use it, please.

 

[stapel]

Lol, I know what the ubside down U is....

Great. Then please display your knowledge by using proper terminology, such as "S-intersect-T", and by defining your abbreviations (does "bd" mean "boundary", or something else?) and your terms (how does your particular text define "boundary"?) and showing your work and reasoning.

I look forward to seeing what you've tried so far.

Eliz.