Metrics Flashcards
1
Q
Define a metric space
A
2
Q
Define an open set in a metric space
A
3
Q
Define a closed set
A
4
Q
Define a neighbourhood
A
5
Q
Describe how open and closed sets behave under union and intersection?
A
(b) an arbitrary union of open sets is open.
1
(c) a finite intersection of open sets is open.
(d) a finite union of closed sets is closed.
(e) an arbitrary intersection of closed sets is closed
6
Q
Give the lemma for when N is neighbourhood in a metric space
A
7
Q
Give the definition of convergence of a sequence
A
8
Q
Give 3 definitions of continuity
A
9
Q
Give continuity in terms of sets
A
10
Q
A
