Question

c) S
4) In a metric space, which of the following is false
a) An arbitrary union of closed sets is closed
b) An arbitrary union of open set is open
c) A countable union of open set is open
d) An intersection of closed set is closed​

Answer 1

Step-by-step explanation:

one third of a number plus 5 in 8

Answer 2

METRIC SPACES

In a metric space, AN ARBITRARY UNION OF CLOSED SETS IS CLOSED.

FEATURES OF METRIC SPACES:

In mathematics, particularly topology, metric space is an abstract set with a distance function, termed a metric, that specifies a non negative distance between any two of its points while maintaining the following properties:

(1) The distance between the first and second points equals zero if and only if the points are the same,

(2) the distance between the second and the first equals the distance between the second and the first, and

(3) the sum of the distances between the first and second points exceeds or equals the distance between the first and the third.