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



"Cohomology at the infinity": what does one call it
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*](http://www.maths.ed.ac.uk/~aar/books/ends.pdf) (CUP, 1996).


