In mathematical logic, descriptive set theory is the study of certain classes of "well-behaved" subsets of the real line and other Polish spaces. As well as being one of the primary areas of research in set theory, it has applications to other areas of mathematics such as functional analysis, ergodic theory, the study of operator algebras and group actions, and mathematical logic.
Read more about Descriptive Set Theory: Polish Spaces, Borel Sets, Analytic and Coanalytic Sets, Projective Sets and Wadge Degrees, Borel Equivalence Relations, Effective Descriptive Set Theory
Famous quotes containing the words set and/or theory:
“You should try to understand every thing you see and hear; to act and judge for yourselves; to remember you each have a soul of your own to account for; M a mind of your own to improve. When you once get these ideas fixed, and learn to act upon them, no man or set of men, no laws, customs, or combinations of them can seriously oppress you.”
—Jane Grey Swisshelm (1815–1884)
“There is in him, hidden deep-down, a great instinctive artist, and hence the makings of an aristocrat. In his muddled way, held back by the manacles of his race and time, and his steps made uncertain by a guiding theory which too often eludes his own comprehension, he yet manages to produce works of unquestionable beauty and authority, and to interpret life in a manner that is poignant and illuminating.”
—H.L. (Henry Lewis)