Objects Defined in Terms of Bases
- The order topology is usually defined as the topology generated by a collection of open-interval-like sets.
- The metric topology is usually defined as the topology generated by a collection of open balls.
- A second-countable space is one that has a countable base.
- The discrete topology has the singletons as a base.
Read more about this topic: Base (topology)
Famous quotes containing the words objects, defined, terms and/or bases:
“Where then shall hope and fear their objects find?”
—John Ashbery (b. 1927)
“The depth and strength of a human character are defined by its moral reserves. People reveal themselves completely only when they are thrown out of the customary conditions of their life, for only then do they have to fall back on their reserves.”
—Leon Trotsky (1879–1940)
“Picture the prince, such as most of them are today: a man ignorant of the law, well-nigh an enemy to his people’s advantage, while intent on his personal convenience, a dedicated voluptuary, a hater of learning, freedom and truth, without a thought for the interests of his country, and measuring everything in terms of his own profit and desires.”
—Desiderius Erasmus (c. 1466–1536)
“In the beginning was the word, the word
That from the solid bases of the light
Abstracted all the letters of the void....”
—Dylan Thomas (1914–1953)