Category:Continuity

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This category contains results about continuity, in all its various contexts.
Definitions specific to this category can be found in Definitions/Continuity.


The mapping $f$ is continuous at (the point) $x$ (with respect to the topologies $\tau_1$ and $\tau_2$) if and only if:

For every open set $U_2$ of $T_2$ such that $\map f x \in U_2$, there exists an open set $U_1$ of $T_1$ such that $x \in U_1$ and $f \sqbrk {U_1} \subseteq U_2$.

Subcategories

This category has the following 14 subcategories, out of 14 total.