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:
“When I consider the short duration of my life, swallowed up in the eternity before and after, the little space which I fill and even can see, engulfed in the infinite immensity of spaces of which I am ignorant and which know me not, I am frightened and am astonished at being here rather than there. For there is no reason why here rather than there, why now rather than then.”
—Blaise Pascal (1623–1662)
“Neatness begets order; but from order to taste there is the same difference as from taste to genius, or from love to friendship.”
—Johann Kaspar Lavater (1741–1801)
“When a house is tottering to its fall,
The strain lies heaviest on the weakest part,
One tiny crack throughout the structure spreads,
And its own weight soon brings it toppling down.”
—Ovid (Publius Ovidius Naso)