Topology MOC

Topological property

A topological property is any property preserved under homeomorphism. topology In general, any property that can be defined in terms of open neighbourhoods only is topological, since these are preserved by homeomorphism.

Since Functors encode invariants of isomorphism classes, the value an arbitrary functor assigns to any topological space is immediately a topological property.

A related concept is a Local property, which is preserved under Local homeomorphism.

Some topological properties

• Cardinality of a topology

• Connectedness

  • Connectedness
  • Path connectedness
  • Local (path) connectedness

• Compactness

  • Compact space
  • Locally compact space

Axiomatic topology

• Countability axioms
• Separation axioms

---

develop | en | sembr