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:
“It is an inexpressible Pleasure to know a little of the World, and be of no Character or Significancy in it. To be ever unconcerned, and ever looking on new Objects with an endless Curiosity, is a Delight known only to those who are turned for Speculation: Nay, they who enjoy it, must value things only as they are the Objects of Speculation, without drawing any worldly Advantage to themselves from them, but just as they are what contribute to their Amusement, or the Improvement of the Mind.”
—Richard Steele (1672–1729)
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“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)