locally convex space sentence in Hindi
"locally convex space" meaning in Hindi locally convex space in a sentenceExamples
- A metrizable locally convex space X is stereotype if and only if X is complete.
- Fr�chet spaces are locally convex spaces that are complete with respect to a translation invariant metric.
- In particular, the following functional spaces frequently used in functional analysis are reflexive locally convex spaces:
- A locally convex space carries a natural topology, called the initial topology induced by the seminorms.
- If X is a pseudocomplete locally convex space, then its pseudosaturation X ^ \ vartriangle is stereotype.
- |3 = As with any topological vector space, a locally convex space is also a uniform space.
- Dually, if X is a pseudosaturated locally convex space, then its pseudocompletion X ^ \ triangledown is stereotype.
- |4 = A Cauchy net in a locally convex space is a complete if and only if every Cauchy net converges.
- The "'Bourbaki Alaoglu theorem "'is a generalization by Bourbaki to dual topologies on locally convex spaces.
- However, the theory of locally convex spaces is not pre-supposed and the requisite material is developed in a short appendix.
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