Local property

It is said in mathematical topology, a property of topological spaces applies locally for a topological space T, if for every choice of a point x in T is a basis of neighborhoods of x exists whose elements have the property.

A topological feature space is local if it agrees with the corresponding local property.

Examples

Local properties:

• Steady

Times the local characteristic is less than the original:

• Locally contractible is weaker than contractible
• Locally compact is weaker than compact
• Locally Hausdorff spaces are not necessary Hausdorff

Sometimes, the local property is stronger than the original:

• Locally simply connected is stronger than semi- locally simply connected

In general, the local property is neither stronger nor weaker:

• The comb is path-connected, locally path-connected but not, the discrete two-element space is locally path-connected topologisierte, but not path-connected.
• A system of subsets of a topological space is called locally finite if every point has a neighborhood that only finitely many touches of the subsets.
• A topological space is locally metrizable if every point has a metrizable environment.