montel space meaning in Hindi

Examples

1. 4 ) Montel spaces are reflexive locally convex topological vector spaces.
2. An infinite-dimensional Montel space is never normable.
3. These are all examples of Montel spaces.
4. The weak dual of a separable Fr�chet space and the strong dual of a separable Fr�chet-Montel space are Souslin spaces.
5. :* X is a Montel space \ Longleftrightarrow X is barreled and has the Heine-Borel peoperty \ Longleftrightarrow X ^ \ star is a Montel space;
6. :* X is a Montel space \ Longleftrightarrow X is barreled and has the Heine-Borel peoperty \ Longleftrightarrow X ^ \ star is a Montel space;
7. No matter what dual topology is placed on D2 ( " U " ), a " sequence " of distributions converges in this topology if and only if it converges pointwise ( although this need not be true of a nuclear Montel space and it is with this topology that the kernels theorem of Schwartz holds.