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Clash Royale CLAN TAG #URR8PPP up vote 1 down vote favorite I am a little bit confused. Assume that $Y$ is a subset of $X$, with the inherited topology from $X$. What does it mean the $Ksubset Y$ is a relatively compact subset of $Y$? One option, is that $K= Ccap Y$, where $C$ is a relatively compact subset in $X$. Another option, is the $overlineKcap Y$ is compact in $Y$. To be specific, I am looking on the following example: Let $X$ be a topological (locally compact Hausdorff), $D_n_ ninmathbbZ$ be a sequence of open subsets inside $X$. For every $n$, let $T_n: D_nto D_-n$ be a homeomorphism. Consider the set $Y:= xin D_n$ with the inherited topology from $Xtimes mathbbZtimes X$. I want to say that if $Ksubset Y$ is relatively compact, then $K$ is contained in a set of the form $(T_n(x),n,x)in Xtimes mathbbZtimes X$ for some relatively compact set $C$ in $X$ and $NinmathbbN$. Is it true? Thanks! general-topology compactness share | cite | improve this question

Clash Royale CLAN TAG #URR8PPP up vote 0 down vote favorite Let $T colon mathbbC to mathbbC$ be an $mathbbR$-linear map. Show that there exists complex numbers $lambda, mu$ such that one has $T(z) = lambda z + mu overlinez$ and show that $lambda, mu$ are uniquely determined by $T$, by giving explicit expressions of $lambda, mu$ in terms of $T(1)$ and $T(i)$. Have no idea how to start the proof! Pls help! complex-analysis share | cite | improve this question edited Aug 25 at 13:21 Jendrik Stelzner 7,572 2 10 37 asked Aug 25 at 11:25 Jeez 37 5 closed as off-topic by Scientifica, Jendrik Stelzner, Brahadeesh, Gibbs, amWhy Aug 26 at 18:15 This question appears to be off-topic. The users who voted to close gave this specific reason: " This question is missing context or other details : Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made t