Properties Preserved By Equivalence
- The continuity of a function is preserved if either the domain or range is remetrized by an equivalent metric, but uniform continuity is preserved only by strongly equivalent metrics.
- The differentiability of a function is preserved if either the domain or range is remetrized by a strongly equivalent metric.
Read more about this topic: Equivalence Of Metrics
Famous quotes containing the words properties and/or preserved:
“A drop of water has the properties of the sea, but cannot exhibit a storm. There is beauty of a concert, as well as of a flute; strength of a host, as well as of a hero.”
—Ralph Waldo Emerson (1803–1882)
“You are told a lot about your education, but some beautiful, sacred memory, preserved since childhood, is perhaps the best education of all. If a man carries many such memories into life with him, he is saved for the rest of his days. And even if only one good memory is left in our hearts, it may also be the instrument of our salvation one day.”
—Feodor Dostoyevsky (1821–1881)