Verify that the following statement is true if the blank is

Verify that the following statement is true if the blank is filled with the word \"finite.\" Do this again with the word \"compact.\" Also, do this with the word \"closed.\"

Solution

according to FINITE INTERSECTION PROPERTY the collection should be CLOSED and infinite.

also we know that that a set X is compact iff X satisfies finite intersection property.

thus the result is true for closed and compact but not for finite sets