Articles by Author: B Banaschewski

Search results for B Banaschewski

We found 21 results for you
  1. On Lindel¨of uniform frames and the axiom of countable choice

    On Lindel¨of uniform frames and the axiom of countable choice

    Item type: Journal Article • Journal: Quaestiones Mathematicae
    This paper takes another look at the result that any complete separable uniform frame is Lindelöf and some of its ramifications. In particular, it shows that this is equivalent to the axiom of countable choice and provides a new, considerably...
  2. On the sheaf characterization of Gelfand rings

    On the sheaf characterization of Gelfand rings

    Item type: Journal Article • Journal: Quaestiones Mathematicae
    This paper deals with the commutative rings with unit in which a+b = 1 implies that (1+ar)(1+bs) = 0 for suitable r and s. These rings have been considered, alternatively, in terms of conditions on their maximal ideals (DeMarco-Orsatti 1971,...
  3. The spectral theory of commutative C<sup>*</sup>-algebras: The constructive spectrum

    The spectral theory of commutative C<sup>*</sup>-algebras: The constructive spectrum

    Item type: Journal Article • Journal: Quaestiones Mathematicae
    This paper introduces the notion of a commutative C*-algebra in a Grothendieck topos E and subsequently that of the spectrum MFn A of A, presented as the locale determined by an appropriate propositional theory in the topos E which describes...
  4. The spectral theory of commutative C<sup>*</sup>-algebras: The constructive Gelfand-Mazur theorem

    The spectral theory of commutative C<sup>*</sup>-algebras: The constructive Gelfand-Mazur theorem

    Item type: Journal Article • Journal: Quaestiones Mathematicae
    It is shown, for a commutative C*-algebra in any Grothendieck topos E, that the locale MFn A of multiplicative linear functionals on A is isomorphic to the locale Max A of maximal ideals of A, extending the classical result that...
  5. SHEAVES OF BANACH SPEACES

    SHEAVES OF BANACH SPEACES

    Item type: Journal Article • Journal: Quaestiones Mathematicae
    This paper presents a number of results concerning sheaves on a topological space, with values in the category BAN of Banach spaces, over K = R or Ø, and linear contractions. After showing that these sheaves are reflective in the...
  6. WHEN ARE DIVISIBLE ABELIAN GROUPS INJECTIVE?

    WHEN ARE DIVISIBLE ABELIAN GROUPS INJECTIVE?

    Item type: Journal Article • Journal: Quaestiones Mathematicae
    The above question is considered, in the categories ShL of sheaves on a local lattice L and MEns of sets acted upon by a monoid M, for either all divisible abelian groups or all torsionfree divisible abelian groups, the aim...
  7. ON LATTICES OF CONTINUOUS FUNCTIONS

    ON LATTICES OF CONTINUOUS FUNCTIONS

    Item type: Journal Article • Journal: Quaestiones Mathematicae
    A detailed study is made of the contravariant functor D which assigns to each compact Hausdorff space X the bounded distributive lattice DX of all functions on X with values in the unit interval, and of some variants of D...
  8. BIFRAMES AND BISPACES

    BIFRAMES AND BISPACES

    Item type: Journal Article • Journal: Quaestiones Mathematicae
    The concept of a biframe is introduced. Then the known dual adjunction between topological spaces and frames (i.e. local lattices) is extended to one between bispaces (i.e. bitopological spaces) and biframes. The largest duality contained in this dual adjunction defines...
  9. THOUGHTS ON THE CANTOR-BERNSTEIN THEOREM

    THOUGHTS ON THE CANTOR-BERNSTEIN THEOREM

    Item type: Journal Article • Journal: Quaestiones Mathematicae
    The usual proofs of the well-known set-theoretical theorem “Given one-one maps f: A → B and g:B → A, there exists a one-one onto map h:A → B” actually produce a map h:A → B contained in the relation f...
  10. STRONG ZERO-DIMENSIONALITY OF BIFRAMES AND BISPACES

    STRONG ZERO-DIMENSIONALITY OF BIFRAMES AND BISPACES

    Item type: Journal Article • Journal: Quaestiones Mathematicae
    A bispace is called strongly zero-dimensional if its bispace Stone—Čech compactification is zero—dimensional. To motivate the study of such bispaces we show that among those functorial quasi—uniformities which are admissible on all completely regular bispaces, some are and others are...