Infinite Dimensions
Researchers have also considered Hilbert's fifth problem without supposing finite dimensionality. The last chapter of Benyamini and Lindenstrauss discuss the thesis of Per Enflo, on Hilbert's fifth problem without compactness.
Read more about this topic: Hilbert's Fifth Problem
Famous quotes containing the words infinite and/or dimensions:
“One who pressed forward incessantly and never rested from his labors, who grew fast and made infinite demands on life, would always find himself in a new country or wilderness, and surrounded by the raw material of life. He would be climbing over the prostrate stems of primitive forest-trees.”
—Henry David Thoreau (1817–1862)
“The truth is that a Pigmy and a Patagonian, a Mouse and a Mammoth, derive their dimensions from the same nutritive juices.... [A]ll the manna of heaven would never raise the Mouse to the bulk of the Mammoth.”
—Thomas Jefferson (1743–1826)