| slovo | definícia |
banach
(encz) | Banach,Banach n: [jmén.] příjmení Zdeněk Brož a automatický překlad |
banach
(czen) | Banach,Banachn: [jmén.] příjmení Zdeněk Brož a automatický překlad |
| | podobné slovo | definícia |
banach algebra
(foldoc) | Banach algebra
An algebra in which the vector space is a
Banach space.
(1997-02-25)
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banach inverse mapping theorem
(foldoc) | Banach inverse mapping theorem
In a Banach space the inverse to a
continuous linear mapping is continuous.
(1998-06-25)
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banach space
(foldoc) | Banach space
A complete normed vector space. Metric is
induced by the norm: d(x,y) = ||x-y||. Completeness means
that every Cauchy sequence converges to an element of the
space. All finite-dimensional real and complex normed
vector spaces are complete and thus are Banach spaces.
Using absolute value for the norm, the real numbers are a
Banach space whereas the rationals are not. This is because
there are sequences of rationals that converges to
irrationals.
Several theorems hold only in Banach spaces, e.g. the {Banach
inverse mapping theorem}. All finite-dimensional real and
complex vector spaces are Banach spaces. Hilbert spaces,
spaces of integrable functions, and spaces of {absolutely
convergent series} are examples of infinite-dimensional Banach
spaces. Applications include wavelets, signal processing,
and radar.
[Robert E. Megginson, "An Introduction to Banach Space
Theory", Graduate Texts in Mathematics, 183, Springer Verlag,
September 1998].
(2000-03-10)
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banach-tarski paradox
(foldoc) | Banach-Tarski paradox
It is possible to cut a solid ball into finitely
many pieces (actually about half a dozen), and then put the
pieces together again to get two solid balls, each the same
size as the original.
This paradox is a consequence of the Axiom of Choice.
(1995-03-29)
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