Editing Local property (section)

==Properties of a single space==

A [[topological space]] is sometimes said to exhibit a property '''locally''', if the property is exhibited "near" each point in one of the following ways:

# Each point has a [[neighbourhood (mathematics)|neighborhood]] exhibiting the property;
# Each point has a [[neighborhood base]] of sets exhibiting the property.

Here, note that condition (2) is for the most part stronger than condition (1), and that extra caution should be taken to distinguish between the two. For example, some variation in the definition of [[locally compact]] can arise as a result of the different choices of these conditions.

===Examples===

* [[Locally compact space|Locally compact]] topological spaces
* [[Locally connected]] and [[Locally path-connected]] topological spaces
* [[Locally Hausdorff space|Locally Hausdorff]], Locally regular, [[Locally normal space|Locally normal]] etc...
* [[Locally metrizable space|Locally metrizable]]