[[Topology MOC]]
# Topological property
A **topological property** is any property preserved under homeomorphism. #m/def/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 $F : \Top \to \cat C$ 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]]

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