a) A set U in a metric space is open if for every x in U there exists epsilon>0 so that B(x,epsilon) is contained in U.

b) (a,b) is always open

c) A set is open if it is in the topology Tau

d) a) and b)

e) a) and c)

b) 2. and 3.

c) 1. 2. and 3.

d) 1. 2. and 4.

e) 2. 3. and 4.

a) Take finite unions and arbitrary intersections and add those to the collection

b) If necessary, add X to the collection

c) Both of the above

d) Other

a) An efficient way to represent a vector space

b) A maximum linearly independent set

c) A minimum spanning set

d) All of the above

e) Other