Definition:Connected (Topology)/Topological Space/Definition 1

From ProofWiki
Jump to navigation Jump to search

Definition

Let $T = \left({S, \tau}\right)$ be a topological space.


$T$ is connected if and only if it admits no separation.


That is, $T$ is connected if and only if there exist no open sets $A, B \in \tau$ such that $A, B \ne \varnothing$, $A \cup B = S$ and $A \cap B = \varnothing$.


Also see

  • Results about connected spaces can be found here.


Sources