List of properties of sets of reals

This page 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