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

See also