List of types of sets

Sets can be classified according to the properties they have.

Relative to set theory

 * Empty set
 * Finite set, Infinite set
 * Countable set, Uncountable set
 * Power set

Relative to a topology

 * Closed set
 * Open set
 * Clopen set
 * Fσ set
 * Gδ set
 * Compact set
 * Relatively compact set
 * Regular open set, regular closed set
 * Connected set
 * Perfect set
 * Meagre set
 * Nowhere dense set

Relative to a metric

 * Bounded set
 * Totally bounded set

Relative to measurability

 * Borel set
 * Baire set
 * Measurable set, Non-measurable set
 * Universally measurable set

Relative to a measure

 * Negligible set
 * Null set
 * Haar null set

In a linear space

 * Convex set
 * Balanced set, Absolutely convex set

Relative to the real/complex numbers

 * Fractal set

Ways of defining sets/Relation to descriptive set theory

 * Recursive set
 * Recursively enumerable set
 * Arithmetical set
 * Diophantine set
 * Hyperarithmetical set
 * Analytical set
 * Analytic set, Coanalytic set
 * Suslin set
 * Projective set
 * Inhabited set

More general objects still called sets

 * Multiset