Teaching MPPSC Assistant Professor Mock Test Series 2025 Mathematical Science Analysis Metric Spaces
If Bx(⋅) and By(⋅) denote open balls in space X and Y respectively, f is continuous at x if
1
There exists ε > 0 such that f[Bx(x : δ)] ⊆ By[f(x), ε]
2
There exists δ > 0 such that f[Bx(x : δ)] ⊆ By[f(x), ε]
3
There exists ε > 0 such that f[Bx(x : δ)] ⊇ By[x, ε]
4
There exists δ > 0 such that f[Bx(x : δ)] ⊇ By[x, ε]