Please give an example in $ \mathbb{R}^{n} $ of a set that satisfies the upper bound in the Kuratowski Closure-Complement Theorem.

Question

Please give an example in $ \mathbb{R}^{n} $ of a set $ T $ that satisfies the upper bound of $ 14 $ in the Kuratowski Closure-Complement Theorem. Thanks!

You may wish to refer to my answer in the following thread: http://math.stackexchange.com/questions/315252/how-to-prove-that-textint-textcla-textcl-textinta/315276#315276. — Haskell Curry, Mar 01 '13 at 22:36

score 4 · Accepted Answer · answered Mar 01 '13 at 22:12

4

The standard example in $ \mathbb{R} $ is $$ (0,1) \cup (1,2) \cup \{ 3 \} \cup [(4,5) \cap \mathbb{Q}]. $$

You can refer to the Wikipedia article on the Kuratowski Closure-Complement Theorem.

answered Mar 01 '13 at 22:12

Haskell Curry

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However, the OP is asking for an example in $\mathbb{R}^{n}$. Is it trivial to construct such one from that in $\mathbb{R}$? – hengxin Jan 22 '14 at 05:11

Please give an example in $ \mathbb{R}^{n} $ of a set that satisfies the upper bound in the Kuratowski Closure-Complement Theorem.

1 Answers1