Is \((0,1)\cup\{2\}\) open or closed?

At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get our expert's

answer on brainly

SEE EXPERT ANSWER

Get your free account and access expert answers to this and thousands of other questions.

A community for students.

Is \((0,1)\cup\{2\}\) open or closed?

Mathematics
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get this expert

answer on brainly

SEE EXPERT ANSWER

Get your free account and access expert answers to this and thousands of other questions

Howcome? :(
i would not say open because the complement is not closed
This is what I did:

Not the answer you are looking for?

Search for more explanations.

Ask your own question

Other answers:

open it is
depends on your definition of open but one definition is for every element in A there is an open neighborhood contained in A that is not the case for the number 2
A is open if \[\forall x \in A \exists \epsilon\text { such that } (x-\epsilon,x+\epsilon)\in A\]
also clearly not closed, since it does not contain all its limit points (namely 0 and 1)
Theorem: If a set \(A\) has an isolated point, then it cannot be an open set. Proof: Let \(a\in A\) be an isolated point in A. Then there exists an \(\epsilon\)-neighborhood \(V_{\epsilon}(a)\) such that \(V_{\epsilon}(a)\cap A=\{a\}\). It follows that \(A\) cannot be open since there exists no \(\epsilon\)-neighborhood \(V_{\epsilon}(a)\) such that \(V_{\epsilon}(a)\subseteq A\). \(\blacksquare\)
(with \(\epsilon>0\), that is)

Not the answer you are looking for?

Search for more explanations.

Ask your own question