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  • 1
    Call number: 1.7/M 07.0295
    Type of Medium: Monograph available for loan
    Pages: XXIV, 1693 S. + 1 CD-ROM
    Edition: 3., aktualisierte Aufl.
    ISBN: 3804116191
    Location: Reading room
    Branch Library: GFZ Library
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Applied categorical structures 4 (1996), S. 361-370 
    ISSN: 1572-9095
    Keywords: 18A20 ; 52A01 ; Convex space ; cogenerator ; (pre-)separated space ; superconvex space ; totally convex space
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We construct a cogenerator for the category of preseparated superconvex spaces, and we describe separated convex spaces, i.e. convex spaces for which the morphisms into the unit interval separates points.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Applied categorical structures 6 (1998), S. 333-344 
    ISSN: 1572-9095
    Keywords: ((pre)separated) (finitely) positively convex space ; regularly ordered Banach space
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We give a construction of the left adjoint of the comparison functor $$\widehat\Delta :Ban_{\text{1}}^{\text{ + }} \to PC {\text{(resp}}{\text{. }}\widehat\Delta _{{\text{fin}}} {\text{: }}Vec_{\text{1}}^{\text{ + }} \to PC_{{\text{fin}}} {\text{)}}$$ in one step and we give a characterization of separated (finitely) positively convex spaces.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Springer
    Applied categorical structures 8 (2000), S. 579-593 
    ISSN: 1572-9095
    Keywords: p-Banach space ; p-normed vector space ; p-totally convex space ; p-absolutely convex space ; comparison functor ; congruence relation ; Eilenberg–Moore category ; monad
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We show that the results about the set S : ={β ∈[0, 1] ∣ β1 / p x + (1 − β)1 / p z ∼ β1 / p y + (1 − β)1 / p z}, where x, y, z elements of a p-absolutely convex space D and `∼' is a congruence relation on D are the best possible. Finally, we give an explicit construction of the left adjoint of the comparison functor Ô p : B an p → T C p (resp. Ô p, fin : V ec p → A C p ).
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    Springer
    Applied categorical structures 6 (1998), S. 345-354 
    ISSN: 1572-9095
    Keywords: injective object ; epi-projective object ; (super) convex space ; (finitely) positively convex space ; absolutely convex space ; totally convex space
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We give a characterization of injective and epi-projective objects in some categories of convex spaces.
    Type of Medium: Electronic Resource
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  • 6
    Electronic Resource
    Electronic Resource
    Springer
    Applied categorical structures 7 (1999), S. 279-295 
    ISSN: 1572-9095
    Keywords: p-Banach space ; p-normed vector space ; (p-) totally (resp. (p-) absolutely) convex space ; congruence relation ; Eilenberg–Moore category ; monad
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We introduce the categories Vec p of p-normed vector spaces, Ban p of p -Banach spaces, AC p of p -absolutely and TC p of p -totally convex spaces (0 〈 p ≤ 1). It will be shown that TC p (AC p ) is the Eilenberg–Moore category of Ban p (Vec p ). Then congruence relations on TC p (AC p )-spaces are studied. There are many differences between TC p (AC p )-spaces and totally (absolutely) convex spaces (i.e. p = 1) (Pumplün and Röhrl, 1984, 1985), which will become apparent in Section 4.
    Type of Medium: Electronic Resource
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  • 7
    Electronic Resource
    Electronic Resource
    Springer
    Applied categorical structures 2 (1994), S. 1-11 
    ISSN: 1572-9095
    Keywords: 18A99 ; 18C05 ; 52A01 ; 52A03 ; Cogenerator ; (absolutely) convex space ; affine map
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We give cogenerators for the categories of convex (= finitely superconvex), finitely positively convex, and absolute convex (= finitely totally convex) spaces introduced by Pumplün and Röhrl.
    Type of Medium: Electronic Resource
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  • 8
    Electronic Resource
    Electronic Resource
    Springer
    Applied categorical structures 3 (1995), S. 363-370 
    ISSN: 1572-9095
    Keywords: 18A20 ; 18C20 ; epimorphism ; (separated) totally convex space ; (pre)separated absolutely convex space
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We give characterizations of the epimorphisms in the categories of open and separated totally convex and (pre)separated absolutely convex spaces.
    Type of Medium: Electronic Resource
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  • 9
    Electronic Resource
    Electronic Resource
    Springer
    Applied categorical structures 5 (1997), S. 217-228 
    ISSN: 1572-9095
    Keywords: epimorphism ; (separated) superconvex space ; (pre)separated convex space
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We give characterizations of the epimorphisms in the categories of (pre)separated convex and separated superconvex spaces.
    Type of Medium: Electronic Resource
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