Biequivalence vector spaces in the alternative set theory
Šmíd, Miroslav ; Zlatoš, Pavol
Commentationes Mathematicae Universitatis Carolinae, Tome 32 (1991), p. 517-544 / Harvested from Czech Digital Mathematics Library
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As a counterpart to classical topological vector spaces in the alternative set theory, biequivalence vector spaces (over the field $Q$ of all rational numbers) are introduced and their basic properties are listed. A methodological consequence opening a new view towards the relationship between the algebraic and topological dual is quoted. The existence of various types of valuations on a biequivalence vector space inducing its biequivalence is proved. Normability is characterized in terms of total convexity of the monad and/or of the galaxy of $0$. Finally, the existence of a rather strong type of basis for a fairly extensive area of biequivalence vector spaces, containing all the most important particular cases, is established.

Publié le : 1991-01-01
Classification:  03E70,  03H05,  46A04,  46A06,  46A08,  46A09,  46A35,  46Q05,  46S20 
@article{118431,
     author = {Miroslav \v Sm\'\i d and Pavol Zlato\v s},
     title = {Biequivalence vector spaces in the alternative set theory},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {32},
     year = {1991},
     pages = {517-544},
     zbl = {0756.03027},
     mrnumber = {1159799},
     language = {en},
     url = {http://dml.mathdoc.fr/item/118431}
}

Šmíd, Miroslav; Zlatoš, Pavol. Biequivalence vector spaces in the alternative set theory. Commentationes Mathematicae Universitatis Carolinae, Tome 32 (1991) pp. 517-544. http://gdmltest.u-ga.fr/item/118431/

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