In topology and related areas of mathematics comparison of topologies refers to the fact that two topological structures on a given set may stand in relation to each other. The set of all possible topologies on a given set forms a partially ordered set. This order relation can be used to compare the different topologies.
Read more about Comparison Of Topologies: Definition, Examples, Properties, Lattice of Topologies
Famous quotes containing the words comparison of and/or comparison:
“But the best read naturalist who lends an entire and devout attention to truth, will see that there remains much to learn of his relation to the world, and that it is not to be learned by any addition or subtraction or other comparison of known quantities, but is arrived at by untaught sallies of the spirit, by a continual self-recovery, and by entire humility.”
—Ralph Waldo Emerson (1803–1882)
“From top to bottom of the ladder, greed is aroused without knowing where to find ultimate foothold. Nothing can calm it, since its goal is far beyond all it can attain. Reality seems valueless by comparison with the dreams of fevered imaginations; reality is therefore abandoned.”
—Emile Durkheim (1858–1917)