About 21,400 results
|A CW- approximation of a topological space Y is a weak homotopy equivalence |
where X is a CW-complex. Theorem 7.31. Any space Y has a CW-approximation.
Proof. We may reduce to the case where Y is path-connected by approximating ...
|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 ...
|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) 5n|x<"-Dx/ ... Theorem 7.5.8 (CW- Approximation Theorem
) Given a topological space Y there exists a CW -complex X and a map f : X ...
|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,
|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 ...
|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), ...
|The main drawback is that we need to keep going to subdivisions, which is not |
the case with CW-approximation. Below we shall indicate an application in
proving the cellular approximation theorem itself. We shall then prove the
|Therefore a weak equivalence between G-CW spectra is a homotopy |
equivalence. THEOREM 2.5 (Cellular approximation). Let A be a subcomplex of
a G-CW spectrum E, let F be a G-CW spectrum, and let f : E ——-> F be a map
|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 ...
|The last important theorem in this chapter is the Cellular Approximation Theorem, |
which in a sense is the analogue for CW-complexes of the Simplicial
Approximation Theorem for simplicial complexes. The theorem states that, if /: K -