Typically, at the beginning of linear algebra texts (and often ring-theoretic ones as well), by way of example of structures being discussed, one is told that the set of all continuous (or differentiable) functions forms a vector space/ring , after which all mention of it promptly ceases. My question is the following: does the apparatus of linear algebra/ring theory lead to any serious structural results for sets like these?
2026-03-25 14:23:44.1774448624
Do linear algebra and ring theory give any worthwhile results for spaces of continuous/differentiable functions?
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