TITLE: "Cohomology at the infinity": what does one call it
QUESTION [8 upvotes]: Suppose $X$ is a "good enough" Hausdorff topological space; we assume that $X$ is not compact. Now, for a natural number $k$ and an abelian group $G$, consider the group $\varinjlim_{\substack{U\subseteq X\\ \text{$X\setminus U$ is compact}}} H^k(U,G)$.  
Could you, please, give me a reference to a text where this object is defined? I would like to learn the standard term and notation for it.  
Thank you in advance,
Serge

REPLY [11 votes]: This is the cohomology of $X$ at $\infty$. You'll find a discussion of (singular) homology and cohomology at $\infty$ in Hughes & Ranicki, Ends of Complexes (CUP, 1996).