Teaching MPPSC Assistant Professor Mock Test Series 2025 Mathematical Science Analysis Metric Spaces
Let (x, dx) and (y, dy) be two metric spaces and f: x → Y then f is continuous if
1
For any set A ⊆ Y we have f-1(A) ⊆ X is open
2
For any open set A ⊆ Y we have f-1(A) ⊆ X is closed.
3
For any open set A ⊆ Y we have f-1(A) ⊆ X is also open
4
For any closed set A ⊆ Y we have f-1(A) ⊆ X is open