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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“The reason why men enter into society, is the preservation of their property; and the end why they choose and authorize a legislative, is, that there may be laws made, and rules set, as guards and fences to the properties of all the members of the society: to limit the power, and moderate the dominion, of every part and member of the society.”
—John Locke (1632–1704)
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—Allen Tate (1899–1979)