Which of the following are correct interpretations of open in this
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)
Which of the following collections of sets are in every topology?
a) 1. and 4.
b) 2. and 3.
c) 1. 2. and 3.
d) 1. 2. and 4.
e) 2. 3. and 4.
Given a collection of sets, how do we generate the smallest topology
containing the sets?
a) Take finite unions and arbitrary intersections and add those to the
b) If necessary, add X to the collection
c) Both of the above
In linear algebra, a basis is:
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