# Tagged Questions

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### Is there a Cantor-Schroder-Bernstein statement about surjective maps?

Let $A,B$ be two sets. The Cantor-Schroder-Bernstein states that if there is an injection $f\colon A\to B$ and an injection $g\colon B\to A$, then there exists a bijection $h\colon A\to B$. I was ...
3answers
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### What is a basis for the vector space of continuous functions?

A natural vector space is the set of continuous functions on $\mathbb{R}$. Is there a nice basis for this vector space? Or is this one of those situations where we're guaranteed a basis by invoking ...
3answers
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### What is the set-theoretic definition of a function?

I'm reading through Asaf Karagila's answer to the question What is the Axiom of Choice and Axiom of Determinacy, and while reading the explanation of Bertrand Russell's analogy ("The Axiom of Choice ...
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