Let tau be a topology on a set X and consider A subeX. If x in X is an accumulation point of A if: AA U in τ,x in U=>A cap U contains another point other than x.

Siena Erickson

Siena Erickson

Answered question

2022-11-17

Let τ be a topology on a set X and consider A X. If x X is an accumulation point of A if:
U τ , x U A U contains another point other than x.

Answer & Explanation

Deanna Sweeney

Deanna Sweeney

Beginner2022-11-18Added 14 answers

Here τ represents the standard topology ,namely, the open intervals in R . So take any real x B τ
Is B P contains a number other than x?
Surely yes! because any open interval B contains both rational as well as irrationals, since they are dense
klesstilne1

klesstilne1

Beginner2022-11-19Added 7 answers

Hint: The irrationals are dense in R , and they do not form a closed set.

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