Connected space

In <a href="/facts/Topology/2EqW47cU">topology</a> and related branches of <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, a connected space is a <a href="/facts/Topological_space/v2ut7CbK">topological space</a> that cannot be represented as the <a href="/facts/Union_(set_theory)/KVVXKfWl">union</a> of two or more <a href="/facts/Disjoint_set/nLr8XRVd">disjoint</a> <a href="/facts/Empty_set/ffEk3eA6">non-empty</a> <a href="/facts/Open_(topology)/QfTCIqMu">open subsets</a>. Connectedness is one of the principal <a href="/facts/Topological_properties/vbJR18Sx">topological properties</a> that distinguish topological spaces.
A subset of a topological space 
 
 
 
 X
 
 
 {\displaystyle X}
 
 is a connected set if it is a connected space when viewed as a <a href="/facts/Subspace_topology/NjU6z4Ca">subspace</a> of 
 
 
 
 X
 
 
 {\displaystyle X}
 
.
Some related but stronger conditions are path connected, <a href="/facts/Simply_connected_space/xFlta63J">simply connected</a>, and <a href="/facts/N-connected_space/dbCgWgu3">
 
 
 
 n
 
 
 {\displaystyle n}
 
-connected</a>. Another related notion is <a href="/facts/Locally_connected_space/9qhzYyT7">locally connected</a>, which neither implies nor follows from connectedness.

Connected space open-in-new

Connected space