open mapping theorem meaning in Hindi

Examples

1. The open mapping theorem points to the sharp difference between holomorphy and real-differentiability.
2. The first mathematical monograph on the subject of open mapping theorem, closed graph theorem, and Hahn Banach theorem.
3. In functional analysis, the open mapping theorem states that every surjective continuous linear operator between Banach spaces is an open map.
4. Further, by the open mapping theorem, if there is a bounded linear operator from the Banach space onto the Banach space, then is reflexive.
5. *PM : proof of open mapping theorem, id = 8537 new !-- WP guess : proof of open mapping theorem-- Status:
6. *PM : proof of open mapping theorem, id = 8537 new !-- WP guess : proof of open mapping theorem-- Status:
7. Several important tools of functional analysis which are based on the Baire category theorem remain true in Fr�chet spaces; examples are the closed graph theorem and the open mapping theorem.
8. Alternatively, the maximum modulus principle can be viewed as a special case of the open mapping theorem, which states that a nonconstant holomorphic function maps open sets to open sets.
9. Since a one-to-one map defined on a non-empty open set cannot be constant, the open mapping theorem forces the inverse function ( defined on the image of f ) to be holomorphic.
10. We feel it mathematically impolite using indirect arguments and general principles ( recall that there is the axiom of choice behind the open mapping theorem ) in order to prove the existence of an object that could be easily exhibited.