This article lists some properties of sets of real numbers. The general study of these concepts forms descriptive set theory, which has a rather different emphasis from general topology.
Definability properties Borel set Analytic set C-measurable set Projective set Inductive set Infinity-Borel set Suslin set Homogeneously Suslin set Weakly homogeneously Suslin set Set of uniqueness
Regularity properties Property of Baire Lebesgue measurable Universally measurable set Perfect set property Universally Baire set
Largeness and smallness properties Meager set Comeager set - A comeager set is one whose complement is meager. Null set Conull set Dense set Nowhere dense set