Topological Spaces With Order Structure
- Spectral. A space is spectral if and only if it is the prime spectrum of a ring (Hochster theorem).
- Specialization preorder. In a space the specialization (or canonical) preorder is defined by x ≤ y if and only if cl{x} ⊆ cl{y}.
Read more about this topic: Topological Space
Famous quotes containing the words spaces, order and/or structure:
“Though there were numerous vessels at this great distance in the horizon on every side, yet the vast spaces between them, like the spaces between the stars,—far as they were distant from us, so were they from one another,—nay, some were twice as far from each other as from us,—impressed us with a sense of the immensity of the ocean, the “unfruitful ocean,” as it has been called, and we could see what proportion man and his works bear to the globe.”
—Henry David Thoreau (1817–1862)
“Since [Rousseau’s] time, and largely thanks to him, the Ego has steadily tended to efface itself, and, for purposes of model, to become a manikin on which the toilet of education is to be draped in order to show the fit or misfit of the clothes. The object of study is the garment, not the figure.”
—Henry Brooks Adams (1838–1918)
“There is no such thing as a language, not if a language is anything like what many philosophers and linguists have supposed. There is therefore no such thing to be learned, mastered, or born with. We must give up the idea of a clearly defined shared structure which language-users acquire and then apply to cases.”
—Donald Davidson (b. 1917)