author hoelzl Thu Sep 02 10:14:32 2010 +0200 (2010-09-02) changeset 39072 1030b1a166ef parent 36862 952b2b102a0a permissions -rw-r--r--
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```    12 <H3>The Hahn-Banach Theorem for Real Vector Spaces (Isabelle/Isar)</H3>
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```    14 Author: Gertrud Bauer, Technische Universit&auml;t M&uuml;nchen<P>
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```    16 This directory contains the proof of the Hahn-Banach theorem for real vectorspaces,
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```    17 following H. Heuser, Funktionalanalysis, p. 228 -232.
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```    18 The Hahn-Banach theorem is one of the fundamental theorems of functioal analysis.
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```    19 It is a conclusion of Zorn's lemma.<P>
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```    21 Two different formaulations of the theorem are presented, one for general real vectorspaces
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```    22 and its application to normed vectorspaces. <P>
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```    24 The theorem says, that every continous linearform, defined on arbitrary subspaces
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```    25 (not only one-dimensional subspaces), can be extended to a continous linearform on
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```    26 the whole vectorspace.
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```    29 <HR>
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```    31 <ADDRESS>
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```    32 <A NAME="bauerg@in.tum.de" HREF="mailto:bauerg@in.tum.de">bauerg@in.tum.de</A>
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```    33 </ADDRESS>
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