Properties
The adele ring is a locally compact complete group with respect to its most natural topology. This group is self dual in the sense that it is topologically isomorphic to its group of characters. The adelic ring contains the number or function field as a discrete co-compact subgroup. Similarly, the multiplicative group of adeles, called the group of ideles, is a locally compact group with respect to its topology defined below.
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Famous quotes containing the word properties:
“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)
“The reason why men enter into society, is the preservation of their property; and the end why they choose and authorize a legislative, is, that there may be laws made, and rules set, as guards and fences to the properties of all the members of the society: to limit the power, and moderate the dominion, of every part and member of the society.”
—John Locke (1632–1704)