Polish Spaces
Descriptive set theory begins with the study of Polish spaces and their Borel sets.
A Polish space is a second countable topological space that is metrizable with a complete metric. Equivalently, it is a complete separable metric space whose metric has been "forgotten". Examples include the real line, the Baire space, the Cantor space, and the Hilbert cube .
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Famous quotes containing the words polish and/or spaces:
“‘Then I polish all the silver, which a supper-table lacquers;
Then I write the pretty mottoes which you find inside the
crackers’—”
—Sir William Schwenck Gilbert (1836–1911)
“Every true man is a cause, a country, and an age; requires infinite spaces and numbers and time fully to accomplish his design;—and posterity seem to follow his steps as a train of clients.”
—Ralph Waldo Emerson (1803–1882)