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/sci/ - Science & Math


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7642482 No.7642482 [Reply] [Original]

What would the math look like for opening a closed set?

>> No.7642638

>>7642482
What the fuck ahahaha. Have you ever studied topology because it sounds like you think closed and open sets are little boxes that you can open and close.
If you really wanted to have a closed set become open your have to define a new topology under which that previously closed set is open.
For example you could just take the discrete topology instead of the topology you are currently using and then, bam, your set is now open (as well as closed).

>> No.7642642

>>7642482
Take the compliment of the frontier of the closed set in the closed set to gain its interior, the largest open set contained in the set.

>> No.7642657
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7642657

>>7642482
sorry, I'm dyslexic and it should be:.... putting or finding an opening on a closed set

>>7642638
>>7642642
Okay, say my set was 1,1 how would you go about defining a bridge to 1,<1

>> No.7642742

It would look like removing the boundary from the closure of the set.

>> No.7642749

(0,1)+{0,1}=[0,1]
Seriously, this isn't hard.

>> No.7642804

>>7642657
>Okay, say my set was 1,1 how would you go about defining a bridge to 1,<1
m8 what

>> No.7643335

>>7642657
You mean a complete set of points with boundaries -1 and 1? Dense in R? Compact? Separable? A bridge isn't a real thing.

>> No.7643337

>>7642657
Also, the set {1,1} is equivalent to {1}.
Also, any finite set is closed in R.
Also, this is a silly question.

>> No.7643360

>>7642657
Shut the fuck up stupid namefag, you're the worst fucking poster on /sci/ with this fucking kind of troll post