Teaching JKPSC Lecturership Mock Test Series 2024-25 Mathematical Science Topology Topological spaces and Continuous Functions
We call a topological space T sequentially compact if _______.
1
T is not compact, it has a maximal open cover V without a finite subcover.
2
U be the collection of their complements. By De Morgan's rules, ∪ is a cover of T.
3
It T compact, s ϵ S and ∪ is an open cover of T × S, there is open V ⊂ S containing s such that T × V can be covered by a finite subfamily of ∪.
4
every sequence in T has a convergent subsequence