Excision and restriction in controlled \(K\)-theory (Q2769470)

Controlled algebra was used by \textit{E. K. Pedersen} and \textit{C. A. Weibel} [Lect. Notes Math. 1126, 166-181 (1985; Zbl 0591.55002) and ibid. 1370, 346-361 (1989; Zbl 0674.55006)] and others to give a description of the generalized homology theory associated with the algebraic K-theory spectrum of a ring \(R\) where \(R\) can be a discrete ring or what appears in Waldhausen's algebraic K-theory of spaces.NEWLINENEWLINENEWLINEWhat the author concerns in this paper is to construct a functor \(F\) from the category of locally compact spaces with countable base to spectra which represents the homology theory mentioned above valid for all locally compact spaces with countable base and to prove several properties among which the most important one may be the excision property which states that the following is a homotopy fibration NEWLINE\[NEWLINEF(X\backslash V) \to F(X) \to F(V)NEWLINE\]NEWLINE where \(X\) is a locally compact space and \(V \subset X\) is open.