2 research outputs found
Numerably Contractible Spaces
Numerably contractible spaces play an important role in the theory of
homotopy pushouts and pullbacks. The corresponding results imply that a number
of well known weak homotopy equivalences are genuine ones if numerably
contractible spaces are involved. In this paper we give a first systematic
investigation of numerably contractible spaces. We list the elementary
properties of the category of these spaces. We then study simplicial objects in
this category. In particular, we show that the topological realization functor
preserves fibration sequences if the base is path-connected and numerably
contractible in each dimension. Consequently, the loop space functor commutes
with realization up to homotopy. We give simple conditions which assure that
free algebras over a topological operad are numerably contractible.Comment: 24 page