## Properties of a single space::Local property

### ::concepts

Locally::space Group::property Locally::local Finite::small Circle::subgroup Finitely::spaces**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 **different** senses:

- Each point has a neighborhood exhibiting the property;
- Each point has a neighborhood base of sets exhibiting the property.

Sense (2) is in general stronger than sense (1), and caution must be taken to distinguish between the two senses. For example, some variation in the definition of locally compact arises from different senses of the term *locally*.

### Examples

- Locally compact topological spaces
- Locally connected and Locally path-connected topological spaces
- Locally Hausdorff, Locally regular, Locally normal etc...
- Locally metrizable

**Local property sections**

Intro Properties of a single space Properties of a pair of spaces Properties of infinite groups Properties of finite groups Properties of commutative rings

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