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:
“‘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)
“When I consider the short duration of my life, swallowed up in the eternity before and after, the little space which I fill and even can see, engulfed in the infinite immensity of spaces of which I am ignorant and which know me not, I am frightened and am astonished at being here rather than there. For there is no reason why here rather than there, why now rather than then.”
—Blaise Pascal (1623–1662)