ACIT4330-Page/content/Definitions/Topological Spaces/Terminologies/Connected.md

Definition

A Topological Space is connected if it is not a union of two non-empty Open Sets.

i.e. if you draw the two non-empty Open Sets on the graph, if you have to lift your pen, it will not be connected.

Examples

Not connected:

\langle 0, 1 ] \cup [ 2, 5 \rangle

Connected:

\langle 0, 1 ] \cup [ 0.5, 5 \rangle = \langle 0, 5 \rangle