Question

prove that an interior point of a set is an open set

plz tell the answer fast.....

Answer 1

$<b><u>Hello Friend!!!!</u></b>$




$<u><b>Here Is Your Answer</b></u>$




$<b>Take any x∈Int S. I will show you that there exists a ball Nx around x completely contained in Int SInt S.</b>$



$<b>By assumption, there exists a ball Nx with Nx⊆S. So take any point y∈Nx. As you note, balls are open, so there exists a ball Ny⊆Nx⊆S around yy. But this means by definition that y∈Int S. Thus, if y∈Nx, then y∈Int S, and so Nx⊆Int S, and Int S is open.</b>$




$<b><u>Hope The Above Answer Helped.</b></u>$




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