Continuous Mapping is Sequentially Continuous/Corollary
Jump to navigation Jump to search
Let $X$ and $Y$ be topological spaces.
Let $f$ be continuous (everywhere) on $X$.
Then $f$ is sequentially continuous on $X$.
This follows immediately from the definitions:
- $(1): \quad$ A mapping is sequentially continuous everywhere in $X$ if and only if if it is sequentially continuous at each point
- $(2): \quad$ A mapping is continuous everywhere on $X$ if and only if it is continuous at each point.