0. Preliminaries Flashcards
1
Q
Definition
Open subset of R^n
A
2
Q
Definition
Closed subset of R^n and their properties.
A
3
Q
Lemma 0.1
A set is closed iff.
A
4
Q
Definition 0.2
Sequentially compact.
A
5
Q
Theorem 0.3 (Sequential Heine-Borel)
A
6
Q
Theorem 0.4 (Compact sets in R^n)
A
7
Q
Lemma 0.5
If A is compact and f cts then f(A)…
A
8
Q
Corollary 0.6
If K is compact and f is cts then f is…
A
9
Q
Theorem 0.7
A function f is cts iff.
A
10
Q
Definition
Complete space.
A
11
Q
Proposition 0.8
Space with sup norm is…
A
12
Q
Proposition 0.9
If A is closed subset then C(…)?
A
13
Q
Definition 0.10
Contraction.
A
14
Q
Theorem 0.13 (Contraction Mapping Theorem)
A
