separable space meaning in Hindi

Examples

1. A set of density 5 ! 0 is a separable space.
2. The product of at most continuum many separable spaces is a separable space.
3. The product of at most continuum many separable spaces is a separable space.
4. For, is also a separable space.
5. A space whose set has a countable, dense subset is called a separable space.
6. From this perspective, the natural state space of a boson might seem to be a non-separable space.
7. In particular, every continuous function on a separable space whose image is a subset of a Hausdorff space is determined by its values on the countable dense subset.
8. In practical terms, this means that theorems of algebra and combinatorics are restricted to countable structures, while theorems of analysis and topology are restricted to separable spaces.
9. Non-separable Banach spaces cannot embed isometrically in the separable space, but for every Banach space, one can find a Banach & ndash; Alaoglu theorem.
10. If " X " is a compact separable space, then the space of finite signed Baire measures is the dual of the real Banach space of all continuous real-valued functions on " X ", by the Riesz Markov Kakutani representation theorem.