In
approximation theory
In mathematics, approximation theory is concerned with how function (mathematics), functions can best be approximation, approximated with simpler functions, and with quantitative property, quantitatively characterization (mathematics), characteri ...
, a Haar space or Chebyshev space is a finite-dimensional subspace
of
, where
is a
compact space
In mathematics, specifically general topology, compactness is a property that seeks to generalize the notion of a closed and bounded subset of Euclidean space by making precise the idea of a space having no "punctures" or "missing endpoints", i ...
and
either the
real numbers
In mathematics, a real number is a number that can be used to measure a ''continuous'' one-dimensional quantity such as a distance, duration or temperature. Here, ''continuous'' means that values can have arbitrarily small variations. Every real ...
or the
complex numbers, such that for any given
there is exactly one element of
that approximates
"best", i.e. with minimum distance to
in
supremum norm.
References
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