The purpose of this paper is to give a direct and relatively simple proof of the fact that the coherent homotopy category CH(Top), introduced in 1983 by Yu.T. Lisitsa and S. Mardešić, is isomorphic to the category Ho(pro-Top), obtained by localizing the category pro-Top at level homotopy equivalence
Local coherence
✍ Scribed by Bernhard König
- Publisher
- Elsevier Science
- Year
- 2003
- Tongue
- English
- Weight
- 400 KB
- Volume
- 124
- Category
- Article
- ISSN
- 0168-0072
No coin nor oath required. For personal study only.
✦ Synopsis
We characterize the tree of functions with ÿnite support in terms of deÿnability. This turns out to have various applications: a new kind of tree dichotomy for !1 on the one hand. On the other hand, we prove a re ection principle for trees on !2 under SPFA. This re ection of trees implies stationary re ection.
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