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 .
Read more about this topic: Descriptive Set Theory
Famous quotes containing the words polish and/or spaces:
“The total and universal want of manners, both in males and females, is ... remarkable ... that polish which removes the coarser and rougher parts of our nature is unknown and undreamed of.”
—Frances Trollope (1780–1863)
“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)