Some articles on spaces, metric spaces, compact metric space, space, metric space, compact:
... result to Lipschitz mappings between Euclidean spaces a Lipschitz map ƒ U → Rm, where U is an open set in Rn, is almost everywhere differentiable ... Lipschitz continuous mappings between two metric spaces, and that all have Lipschitz constant bounded by some K ... this implies that the set of real-valued functions on a compact metric space with a particular bound for the Lipschitz constant is a closed and convex subset of the Banach space of continuous functions ...
... open sets, it itself is a closed subset of the reals, and therefore a complete metric space ... the Heine–Borel theorem says that it must be compact ... As a compact totally disconnected Hausdorff space, the Cantor set is an example of a Stone space ...
Famous quotes containing the words space and/or compact:
“The peculiarity of sculpture is that it creates a three-dimensional object in space. Painting may strive to give on a two-dimensional plane, the illusion of space, but it is space itself as a perceived quantity that becomes the peculiar concern of the sculptor. We may say that for the painter space is a luxury; for the sculptor it is a necessity.”
—Sir Herbert Read (18931968)
“... in a history of spiritual rupture, a social compact built on fantasy and collective secrets, poetry becomes more necessary than ever: it keeps the underground aquifers flowing; it is the liquid voice that can wear through stone.”
—Adrienne Rich (b. 1929)