Local (path) connectedness

Locally path connected spaces have identical connected and path-connected components

Let be a locally path-connected topological space. Then for any , is path-connected to iff is connected to . topology

Proof

proof See for example @looseAlgebraischeTopologie2010, p. 46

Corollaries

• A locally path-connected space is path-connected iff it is connected

---

develop | en | sembr