1. Definability properties

2. Regularity properties

3. Largeness and smallness properties

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

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