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+---
+title: Continuity & Convergence
+parent: General Topology
+nav_order: 2
+---
+
+# {{ page.title }}
+
+{% definition Continuity %}
+A mapping $f: X \to Y$ between topological spaces $X$ and $Y$ is called *continuous*,
+if for each open subset $V$ of $Y$ the inverse image $f^{-1}(V)$ is an open subset of $X$.
+{% enddefinition %}
+
+Slogan: continuous $=$ The inverse image of every open subset is open.
+
+{% definition Homeomorphism %}
+Suppose $X$ and $Y$ are topological spaces.
+A mapping $f: X \to Y$ is said to be a *homeomorphism*,
+if $f$ is bijective and both $f$ and the inverse mapping $f^{-1} : Y \to X$ are continuous.
+{% enddefinition %}
+
+## Nets
+
+## Filters