banach inverse mapping theorem
In a Banach space the inverse to a continuous linear mapping is continuous.
- Banach space
a vector space on which a norm is defined that is complete. mathematics 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. […]
- Banach-tarski paradox
banach-tarski paradox mathematics 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)
noun a tree of the genus Virola, of Central America: family Myristicaceae the timber of this tree, used esp in Honduras for turning and construction Historical Examples (Shoshoni and banak I.) “From the custom of piercing the noses for the reception of ornaments.” Sign Language Among North American Indians Compared With That Among Other Peoples […]
devoid of freshness or originality; hackneyed; trite: a banal and sophomoric treatment of courage on the frontier. adjective lacking force or originality; trite; commonplace adjective pertaining to a lord or ruler (banat) in Hungary, Croatia, and thereabouts Word Origin Serbo-Croatian ban ‘lord, ruler’ adj. “trite, commonplace,” 1840, from French banal, “belonging to a manor, common, […]