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Consider the symmetric monoidal category TVS of complete Hausdorff topological vector spaces equipped with the completed projective, injective, or inductive tensor product. Every finite-dimensional ...

[Edited to take into account comments.] Background One approach to the problem of making rigorous various measures on spaces of paths (for example, the Wiener or Feynman measure) is the time-slicing ...

Let $X$ be a compact Hausdorff space. In chapter 3 of Peter Scholze's Lectures on Analytic Geometry he considers the space of signed Radon measures on $X$ equipped with the filtered colimit (aka ...

Let $X$ be a set. Over the Banach fields $F=\mathbb{R}$ or $F=\mathbb{C}$ we can define the Banach space$$\ell^2(X)=\{\xi\colon X\to F\mid \sum_{x\in X}|\xi(x)|^2<\infty\}$$which satisfies a list ...