4. Rudiements of Topology of R^n and Continuity Flashcards
1
Q
Definition 4.1
Closed subset of R^n
A
2
Q
Definition 4.2
Open subset of R^n
A
3
Q
Proposition 4.3
A set is open iff.
A
4
Q
Proposition 4.9
Arbitrary union of x is x
A
5
Q
Definition 4.10
epsilon neighbourhood
A
6
Q
Proposition 4.12
finitie intersection of x is x
A
7
Q
Corollary
4.13
arbitrary intersection of x is x
finite union of x is x
A
8
Q
Continuity in terms of sets
A
9
Q
Theorem 4.15
f : R^n -> R^k is cts everywhere iff.
Proof
A
10
Q
Definition 4.19
Sequentially compact
A
11
Q
Theorem 4.21
a subset of R^n is sequentially compact iff.
Proof
A
12
Q
Theorem 4.22
Continuity preserves…
A
13
Q
Theorem 4.23
Extreme value theorem
A
14
Q
Corollary 4.25
if K is seq. compact and f : K -> R^k is cts then..
EVT
Proof
A
