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.
Read more about this topic: Local Property
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