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Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology.
2
votes
Accepted
Approximations by compact sub-spaces
Q1. Consider the space of rationals $\mathbb{Q}$.
It is the direct limit of the family of finite unions of convergent sequences (including their limits), ordered by inclusion, as a set is closed iff i …
2
votes
Accepted
Spectrum of continuous functions as a semigroup
Since $X$ is discrete every prime ideal in $C_b(X)$ is maximal and so $\operatorname{Spec}C_b(X)$ is just $\beta X$ and you already have two dual extensions of the operation on $X$.