تقرير
Is a monotone union of contractible open sets contractible?
| العنوان: | Is a monotone union of contractible open sets contractible? |
|---|---|
| المؤلفون: | Ancel, Fredric D., Edwards, Robert D. |
| سنة النشر: | 2016 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - General Topology, Mathematics - Algebraic Topology, Mathematics - Geometric Topology, 54D99, 55M99, 55P99, 57N99 |
| الوصف: | This paper presents some partial answers to the following question. QUESTION. If a normal space X is the union of an increasing sequence of open sets U(1), U(2), U(3) ... such that each U(n) contracts to a point in X, must X be contractible? The main results of the paper are: THEOREM 1. If a normal space X is the union of a sequence of open subsets { U(n) } such that the closure of U(n) is contained in U(n+1) and U(n) contracts to a point in U(n+1) for each n > 0, then X is contractible. COROLLARY 2. If a locally compact sigma-compact normal space X is the union of an increasing sequence of open sets U(1), U(2), U(3) ... such that each U(n) contracts to a point in X, then X is contractible. Comment: In the revised version, a proof of Lemma 5 has been added and a few other minor changes have been made. In the second revision a few minor stylistic changes were made |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/1606.05379 |
| رقم الأكسشن: | edsarx.1606.05379 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |