Thus, a Banach space is a vector space with a metric that allows the computation of vector length and distance between vectors and is complete in the sense that a Cauchy sequence of vectors always converges to a well defined limit that is within the space. Banach spaces are named after the Polish mathematician Stefan Banach , who introduced this concept and studied it systematically in — along with Hans Hahn and Eduard Helly. Banach spaces play a central role in functional analysis. In other areas of analysis , the spaces under study are often Banach spaces.

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We'd like to understand how you use our websites in order to improve them. Register your interest. Applying examples of Pol [9] and Kunen [12] one gets that there exist Banach spaces C X over a compact scattered space X such that C X is not weakly K -analytic even not weakly K -countably determined under CH but the weak dual of C X has countable tightness. This is a preview of subscription content, log in to check access. Rent this article via DeepDyve. Topological function spaces , Math.

Google Scholar. Weight of precompact subsets and tightness, J. The weak topology of a Banach space, Trans. A theorem on the weak topology of C X for compact scattered X, Fund. On a question of H. Corson and some related problems, Fund. On the locally convex structure of strict topologies, Math.

Weakly compact operators and DF -spaces, Pacific J. Banach spaces of continuous functions , Warszawa. Applications of set theory to analysis and topology , Thesis, University of Wisconsin-Madison.

Download references. Correspondence to J. Reprints and Permissions. About an example of a Banach space not weakly K -analytic. Serie A. Download citation. Received : 02 March Accepted : 04 March Issue Date : March Search SpringerLink Search.

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Banach space




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