Coanalytic set
Encyclopedia
In the mathematical discipline of descriptive set theory
, a coanalytic set is a set (typically a set of real number
s or more generally a subset of a Polish space
) that is the complement of an analytic set
. Coanalytic sets are also referred to as
sets (see projective hierarchy).
Descriptive set theory
In mathematical logic, descriptive set theory is the study of certain classes of "well-behaved" subsets of the real line and other Polish spaces...
, a coanalytic set is a set (typically a set of real number
Real number
In mathematics, a real number is a value that represents a quantity along a continuum, such as -5 , 4/3 , 8.6 , √2 and π...
s or more generally a subset of a Polish space
Polish space
In the mathematical discipline of general topology, a Polish space is a separable completely metrizable topological space; that is, a space homeomorphic to a complete metric space that has a countable dense subset. Polish spaces are so named because they were first extensively studied by Polish...
) that is the complement of an analytic set
Analytic set
In descriptive set theory, a subset of a Polish space X is an analytic set if it is a continuous image of a Polish space. These sets were first defined by and his student .- Definition :There are several equivalent definitions of analytic set...
. Coanalytic sets are also referred to as
sets (see projective hierarchy).