 About 21,400 results  books.google.com A CW approximation of a topological space Y is a weak homotopy equivalence
where X is a CWcomplex. Theorem 7.31. Any space Y has a CWapproximation.
Proof. We may reduce to the case where Y is pathconnected by approximating ... 

 books.google.com Another problem is that, due to the fibrancy condition in HELP, we cannot use the
Whitehead theorem to deduce that our CW approximations are functorial up to
homotopy (rather than just functorial on homotopy categories) and that T is ... 

 books.google.com Proof of Theorem 7.5.1 It suffices to construct for all n a map gn : X^ x I — > y such
that: 1) 9n\xMxO ~ f; 2) 5nx<"Dx/ ... Theorem 7.5.8 (CW Approximation Theorem
) Given a topological space Y there exists a CW complex X and a map f : X ... 

 books.google.com CW. Complex. 635. 0. The function for xe [— 1, 1]. The INVARIANT DENSITY is
References Beck, C. and Schlogl, ... See also COHOMOLOGY, CW
APPROXIMATION THEOREM, HOMOLOGY GROUP, HOMOTOPY GROUP,
SIMPLICIAL ... 

 books.google.com By theorem 7, g is a weak homotopy equivalence. By corollary 7.6.24, g is a
homotopy equivalence. □ 8 WEAK HOMOTOPY TYPE In this section we shall
show that any space can be approximated by CW complexes. This leads to an ... 

 books.google.com Approximation of excisive triads by CW triads We will need another, and
considerably more subtle, relative approximation theorem. A triad (X; A, B) is a
space X together with subspaces A and B. This must not be confused with a triple
(X, A,B), ... 

 books.google.com The main drawback is that we need to keep going to subdivisions, which is not
the case with CWapproximation. Below we shall indicate an application in
proving the cellular approximation theorem itself. We shall then prove the
Sperner ... 

 books.google.com Therefore a weak equivalence between GCW spectra is a homotopy
equivalence. THEOREM 2.5 (Cellular approximation). Let A be a subcomplex of
a GCW spectrum E, let F be a GCW spectrum, and let f : E ——> F be a map
whose ... 

 books.google.com This, and the analogous function spectrum construction, is all contained in [
LMS86, II, Section 3]. We learn from [LMS86, Lemma 1.5.3] that G/H+ A S is
always small. The CW approximation theorem [LMS86, Chapter I] implies that
any object in ... 

 books.google.com The last important theorem in this chapter is the Cellular Approximation Theorem,
which in a sense is the analogue for CWcomplexes of the Simplicial
Approximation Theorem for simplicial complexes. The theorem states that, if /: K 
*. 

 