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1. On the importance of the relation [(A,B.), (A.C.)] (A, [B,C,) (C.A.), (A,B)] between three elements of a structure ; 2. Komplexe euklidische Raume von beliebiger endliche oder transfiniter Dimensionszahl ; 3. Intrinsic topology and completion of Boolean rings ; 4. Uber die Dimension linearer Raume.

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Lowig, HFJ (1951) 1. On the importance of the relation [(A,B.), (A.C.)] (A, [B,C,) (C.A.), (A,B)] between three elements of a structure ; 2. Komplexe euklidische Raume von beliebiger endliche oder transfiniter Dimensionszahl ; 3. Intrinsic topology and completion of Boolean rings ; 4. Uber die Dimension linearer Raume. DSc thesis, University of Tasmania.

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Abstract

While the Dedekind axiom is identical with its dual counterpart the corresponding assertion about the
equation (2) is not true.
THEOREM 11. In our structure A the equation (10) is generally valid.
The proof follows easily from the dual counterpart of Theorem 9. Of course
Theorem 11 can also be verified simply by the table on p. 576:
THEOREM 12. The assertion that in a structure the equation (2) holds for arbitrary elements, A, B, and C, and the assertion dually corresponding to this assertion are not
equivalent.
PROOF. See Theorem 11.

Item Type: Thesis (DSc)
Keywords: Vector spaces, Boolean rings, Topology
Copyright Holders: The Author
Copyright Information:

Copyright 1951 the Author - The University is continuing to endeavour to trace the copyright owner(s) and in the meantime this item has been reproduced here in good faith. We would be pleased to hear from the copyright owner(s).

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Thesis (D.Sc.)--University of Tasmania, 1951

Date Deposited: 19 Dec 2014 02:30
Last Modified: 05 Jul 2017 06:18
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