Journal of Formalized Mathematics
Volume 5, 1993
University of Bialystok
Copyright (c) 1993 Association of Mizar Users

Hahn-Banach Theorem


Bogdan Nowak
Lodz University
Andrzej Trybulec
Warsaw University, Bialystok

Summary.

We prove a version of Hahn-Banach Theorem.

MML Identifier: HAHNBAN

The terminology and notation used in this paper have been introduced in the following articles [13] [6] [19] [1] [7] [9] [20] [3] [4] [17] [16] [15] [10] [5] [11] [8] [18] [14] [12] [2]

Contents (PDF format)

  1. Preliminaries
  2. Sets Linearly Ordered by the Inclusion
  3. Subspaces of a Real Linear Space
  4. Functionals
  5. Hahn-Banach Theorem

Bibliography

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[2] Jozef Bialas. Infimum and supremum of the set of real numbers. Measure theory. Journal of Formalized Mathematics, 2, 1990.
[3] Czeslaw Bylinski. Functions and their basic properties. Journal of Formalized Mathematics, 1, 1989.
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[5] Czeslaw Bylinski. Partial functions. Journal of Formalized Mathematics, 1, 1989.
[6] Czeslaw Bylinski. Some basic properties of sets. Journal of Formalized Mathematics, 1, 1989.
[7] Krzysztof Hryniewiecki. Basic properties of real numbers. Journal of Formalized Mathematics, 1, 1989.
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[10] Jan Popiolek. Real normed space. Journal of Formalized Mathematics, 2, 1990.
[11] Andrzej Trybulec. Binary operations applied to functions. Journal of Formalized Mathematics, 1, 1989.
[12] Andrzej Trybulec. Domains and their Cartesian products. Journal of Formalized Mathematics, 1, 1989.
[13] Andrzej Trybulec. Tarski Grothendieck set theory. Journal of Formalized Mathematics, Axiomatics, 1989.
[14] Andrzej Trybulec. Function domains and Fr\aenkel operator. Journal of Formalized Mathematics, 2, 1990.
[15] Wojciech A. Trybulec. Operations on subspaces in real linear space. Journal of Formalized Mathematics, 1, 1989.
[16] Wojciech A. Trybulec. Subspaces and cosets of subspaces in real linear space. Journal of Formalized Mathematics, 1, 1989.
[17] Wojciech A. Trybulec. Vectors in real linear space. Journal of Formalized Mathematics, 1, 1989.
[18] Wojciech A. Trybulec. Basis of real linear space. Journal of Formalized Mathematics, 2, 1990.
[19] Zinaida Trybulec. Properties of subsets. Journal of Formalized Mathematics, 1, 1989.
[20] Edmund Woronowicz. Relations and their basic properties. Journal of Formalized Mathematics, 1, 1989.

Received July 8, 1993

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