Is there an analogue of Schauder type fixed point theorems that can be used over a metric linear space. So, here $(X,d)$ is a complete vector space with metric $d$. If $C\subseteq X$ and $f:C\rightarrow C$ is a continuous and compact map. Then does $f$ have a fixed point?
Schauder's fixed point theorem for metric linear space
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metric-spaces
fixed-point-theorems
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0What do you mean by a "compact map" in this context? – 2012-05-18
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0@RobertIsrael By that I mean $f(C)$ is a compact subset of $C$. Thanks for the Wikipedia link. The book I had presented this result only for Banach spaces. I must look more carefully to prove this general result – 2012-05-18