Vocab

Question 1

Compact

Answer 1

Every open cover has a finite subcover

Question 2

Closed

Answer 2

Contains all its own limit points, complement is open

Question 3

Complement

Answer 3

Overarching set minus A

Question 4

Topology

Answer 4

Subset of the power set, finite intersections, arbitrary unions, contains the entire set and the null.

Question 5

Limit point

Answer 5

Any neighborhood of a limit point of A contains a different point of A

Question 6

Open set

Answer 6

Any set that’s in the topology

Question 7

Continuous

Answer 7

Open sets in destination have open preimages in source

Question 8

Connected

Answer 8

Can’t be represented as union of disjoint open sets.

Question 9

Path Connected

Answer 9

There’s an f: [0,1] to A with f(0) = a, f(1) = b, for any a,b in A.

Question 10

Locally Path Connected

Answer 10

Every neighborhood has a path connected subset.

Question 11

Locally Connected

Answer 11

Every neighborhood has a connected subset.

Question 12

Cover

Answer 12

Set of open sets whose union contains the covered set

Question 13

Subcover

Answer 13

Subset of the index of a cover, which still contains the covered set.