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)
“A drop of water has the properties of the sea, but cannot exhibit a storm. There is beauty of a concert, as well as of a flute; strength of a host, as well as of a hero.”
—Ralph Waldo Emerson (1803–1882)
“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)
“[The] elderly and timid single gentleman in Paris ... never drove down the Champs Elysees without expecting an accident, and commonly witnessing one; or found himself in the neighborhood of an official without calculating the chances of a bomb. So long as the rates of progress held good, these bombs would double in force and number every ten years.”
—Henry Brooks Adams (1838–1918)
“There is commonly sufficient space about us. Our horizon is never quite at our elbows.”
—Henry David Thoreau (1817–1862)