# Category:Sequential Continuity

Jump to navigation
Jump to search

This category contains results about **Sequential Continuity**.

Definitions specific to this category can be found in Definitions/Sequential Continuity.

Let $T_1 = \struct {S_1, \tau_1}$ and $T_2 = \struct {S_2, \tau_2}$ be topological spaces.

Let $f: S_1 \to S_2$ be a mapping.

### At a Point

Let $x \in S_1$.

Then $f$ is **sequentially continuous at (the point) $x$** if and only if:

- for every sequence $\sequence {x_n}_{n \mathop \in \N}$ in $T_1$ which converges to $x$, the sequence $\sequence {\map f {x_n} }_{n \mathop \in \N}$ in $T_2$ converges to $\map f x$.

### On a Domain

$f$ is **sequentially continuous on $T_1$** if and only if $f$ is sequentially continuous at $x$ for every $x \in T_1$.

## Subcategories

This category has only the following subcategory.

## Pages in category "Sequential Continuity"

The following 5 pages are in this category, out of 5 total.