weak compactness meaning in Hindi

Examples

1. Although the weak topology of the unit ball is not metrizable in general, one can characterize weak compactness using sequences.
2. In a Hilbert space, the weak compactness of the unit ball is very often used in the following way : every bounded sequence in has weakly convergent subsequences.
3. Weak compactness of the unit ball provides a tool for finding solutions in reflexive spaces to certain convex continuous function on the unit ball of a reflexive space attains its minimum at some point in.
4. A language " L " ?, ? is said to satisfy the weak compactness theorem if whenever ? is a set of sentences of cardinality at most ? and every subset with less than ? elements has a model, then ? has a model.