Articles by Author: B Banaschewski
Search results for B Banaschewski
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On Lindel¨of uniform frames and the axiom of countable choice
Item type: Journal Article • Journal: Quaestiones MathematicaeThis 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... 
On the sheaf characterization of Gelfand rings
Item type: Journal Article • Journal: Quaestiones MathematicaeThis 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 (DeMarcoOrsatti 1971,... 
The spectral theory of commutative C<sup>*</sup>algebras: The constructive spectrum
Item type: Journal Article • Journal: Quaestiones MathematicaeThis 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... 
The spectral theory of commutative C<sup>*</sup>algebras: The constructive GelfandMazur theorem
Item type: Journal Article • Journal: Quaestiones MathematicaeIt 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... 
SHEAVES OF BANACH SPEACES
Item type: Journal Article • Journal: Quaestiones MathematicaeThis 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... 
WHEN ARE DIVISIBLE ABELIAN GROUPS INJECTIVE?
Item type: Journal Article • Journal: Quaestiones MathematicaeThe 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... 
ON LATTICES OF CONTINUOUS FUNCTIONS
Item type: Journal Article • Journal: Quaestiones MathematicaeA 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... 
BIFRAMES AND BISPACES
Item type: Journal Article • Journal: Quaestiones MathematicaeThe 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... 
THOUGHTS ON THE CANTORBERNSTEIN THEOREM
Item type: Journal Article • Journal: Quaestiones MathematicaeThe usual proofs of the wellknown settheoretical theorem “Given oneone maps f: A → B and g:B → A, there exists a oneone onto map h:A → B” actually produce a map h:A → B contained in the relation f... 
STRONG ZERODIMENSIONALITY OF BIFRAMES AND BISPACES
Item type: Journal Article • Journal: Quaestiones MathematicaeA bispace is called strongly zerodimensional 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...