apostol裡的東西

Question

let A be the set of rational number of (0,1), then closure of A=[0,1] 類似這樣的定裡還例子大概在哪個章節或第幾頁 謝謝

Answer 1

Tom Apostal, "Mathematical Analysis", 2nd Ed.
第三章 (Elements of Point Set Topology):
第 3.7 節 (Closed Sets and Adherent Points) 中有
Closure 的定義 (Definition of closure).
接下來是:
3.8 The Bolzano-Weierstrass Theorem
3.9 The Cantor Intersection Theorem
3.10 The Lindelof Covering Theorem
3.11 The Heine-Borel Covering Theorem
3.12 Compactness in R^n
3.13 Metric Spaces
3.14 Point Set Topology in Metric Spaces
3.15 Compact Subsets of a Metric Space
3.16 Boundary of a Set

Answer 2

索引 → "closure"