Space in which the connected components coincide with the quasicomponents

From Topospaces
Jump to: navigation, search

Definition

A space in which the connected components coincide with the quasicomponents is a topological space satisfying the following equivalent conditions:

  1. Each quasicomponent is connected with the subspace topology.
  2. Each connected component is a quasicomponent.
  3. Each quasicomponent is a connected component.
  4. The connected components and quasicomponents coincide.

Relation with other properties

Stronger properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
connected space Space in which all connected components are open|FULL LIST, MORE INFO
space with finitely many connected components Space in which all connected components are open|FULL LIST, MORE INFO
locally connected space Space in which all connected components are open|FULL LIST, MORE INFO
space in which all connected components are open |FULL LIST, MORE INFO