Descriptive Set Theory - Polish Spaces

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:

    Take a commonplace, clean it and polish it, light it so that it produces the same effect of youth and freshness and originality and spontaneity as it did originally, and you have done a poet’s job. The rest is literature.
    Jean Cocteau (1889–1963)

    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)