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Oct 4, 2022 at 7:10 comment added Jochen Wengenroth Why does this answer Q3? The Michael line is centainly not compact. And for general topological spaces $X$, what should boundedness of an extension operator mean? Either one considers other locally convex topologies on $C(X,E)$ like uniform convergence on compact sets or, to stay in the category of Banach spaces, one considers the space $CB(X,E)$ of bounded continuous functions with the supremum norm.
Jun 15, 2020 at 7:27 history edited CommunityBot
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Aug 4, 2019 at 21:53 comment added ABIM Thanks this is a fantastic answer!
Apr 3, 2015 at 17:59 history edited Vidit Nanda CC BY-SA 3.0
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Apr 3, 2015 at 17:39 history answered Vidit Nanda CC BY-SA 3.0