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Prove that the closed interval [a, b] is compact.
I am studying the topology of $\mathbb{R}$ and I want to prove that the closed interval $[a,b]$ is compact using the Heine-Borel Theorem that a set in $\mathbb{R}$ is compact iff it is closed and ...
user1052225
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Example of basis
Excuse me , can you see this question
, the collection of all open intervals (a,b) together with the one-point sets {n} for all positive and negative integers n is a base for a topology on a real ...
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Problem in proof of -"A net has $y$ as a cluster point iff it has a subnet which converges to $y$"
Directed Set:
We say that $(\omega, ≤)$ is a directed set, if ≤ is a relation on $\omega$
such that
(i) x ≤ y ∧ y ≤ z ⇒ x ≤ z for each x, y, z ∈ $\omega$;
(ii) x ≤ x for each x ∈ $\omega$;
(iii) for ...
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