Definition talk:Component (Topology)

The previous statement of the alternative definition was incorrect. Indeed, the empty set (viewed as a topological space) has no connected component, since every connected component is nonempty. However, the empty set itself is a maximal connected subset. -- lasserempe 15:51, 7 March 2009 (UTC)

Not sure about this:
 * The component $$C$$ of $$T$$ containing $$x$$ can be alternatively defined as:


 * $$C = \bigcup\{A\subseteq T: A\text{ is connected}\}$$;

... where's the reference to $$A$$ from $$x$$? Presumably it's supposed to include the info $$\forall A \subseteq T: x \in A$$ in there or something. --Matt Westwood 12:44, 8 March 2009 (UTC)

Oops. -- lasserempe 13:10, 8 March 2009 (UTC)