# Tagged Questions

For questions about the formulation of a proof, not about the mathematics behind it.

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### If $(X, \mathcal{T})$ has a countable subbasis, then it has a countable basis

Given $(X, \mathcal{T})$ a topological space. Let $\mathcal{S}$ be a subbasis on $(X, \mathcal{T})$ Claim: If $\mathcal{S}$ is countable, then $\mathcal{T}$ has a countable basis $\mathcal{B}$ ...
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### Obscure proof that $+$ and $\times$ are continuous?

I am looking for proof of $+$ and $\times$ are continuous operations without using the standard definition of continuity (1. $\epsilon-\delta$, or 2. preimage of open sets or 3. sequential ...
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### How to show that $f(X \backslash f^{-1}(Y \backslash C)) \subseteq C$

Let $f: X \to Y$ be a continuous function, and that $C \subset Y$, then claim: $f(X \backslash f^{-1}(Y \backslash C)) \subseteq C$ Attempt: Immediately we run into a problem following: ...
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### Powers of two in an infinite sequence of arbitrary integers

I'm not sure how to ask this properly and I haven't seen this problem anywhere yet, but I'm still interested if this can be (dis)proven or not. Consider a finite sequence of the numbers 1, 2, 4, and ...
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### Prove $(A \cup B)' = A' \cap B'$

I would like some assistance in verifying this proof? (I understand the last conjecture about "symmetry" is probably shaky, but I just want to know if the first part is right since going backwards ...
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