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:
“Adultery itself in its principle is many times nothing but a curious inquisition after, and envy of another man’s enclosed pleasures: and there have been many who refused fairer objects that they might ravish an enclosed woman from her retirement and single possessor.”
—Jeremy Taylor (1613–1667)
“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)
“One of the most highly valued functions of used parents these days is to be the villains of their children’s lives, the people the child blames for any shortcomings or disappointments. But if your identity comes from your parents’ failings, then you remain forever a member of the child generation, stuck and unable to move on to an adulthood in which you identify yourself in terms of what you do, not what has been done to you.”
—Frank Pittman (20th century)
“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)