Many existence propositions in constructive analysis are implied by the lesser limited principle of omniscience LLPO; sometimes one can even show equivalence. It was discovered recently that some existence propositions are equivalent to Bouwer's fan theorem FAN if one additionally assumes that there exists at most one object with the desired property. We are providing a list of conditions being equivalent to FAN, such as a unique version of weak König's lemma. This illuminates the relation between FAN and LLPO. Furthermore, (...) we give a short and elementary proof of the fact that FAN is equivalent to each positive valued function with compact domain having positive infimum. (shrink)

Qu'Éclane soit le siège de l'évêché de Julien est un fait bien établi. Mais quelle était sa patrie d'origine? Cet article résume un certain nombre de suggestions faites au cours des derniers siècles et jette un oeil neuf sur les sources. Prenant en considération aussi bien le domaine des textes que ceux de l'histoire, de la géographie ou de l'ethnologie, l'auteur arrive à la conclusion qu'Éclane fut non seulement le siège de l'évêché de Julien mais également son lieu de naissance.

Working within Bishop’s constructive framework, we examine the connection between a weak version of the Heine–Borel property, a property antithetical to that in Specker’s theorem in recursive analysis, and the uniform continuity theorem for integer-valued functions. The paper is a contribution to the ongoing programme of constructive reverse mathematics.

Cet article présente une vue d'ensemble de l'histoire de la recherche sur la structure et le sujet de «De vera religione», ainsi que de nouvelles suggestions.

It is shown, with intuitionistic logic, that if every locally constant function from to has a property akin to constancy, then the fan theorem for -bars holds, and conversely.

It is shown that, relative to Bishop-style constructive mathematics, the boundedness principle BD-N is equivalent both to a general result about the convergence of double sequences and to a particular one about Cauchyness in a semi-metric space.

We prove constructively that the weak König lemma and quantifier-free number-number choice imply that every pointwise continuous function from Cantor space into Baire space has a modulus of uniform continuity.

ABSTRACTJan Patočka is known as a philosophical analyst of the phenomenological concept of the live-word, which contradicts the preoccupations expressed in Sir Herbert Read’s Art of Sc...

Smart MR contrast agents exhibit modulation of their relaxivity by specific physiological or biochemical trigger-events, while targeted MR contrast agents are envisioned to deliver the large gadolinium chelates into the target tissue. In an effort to develop novel smart and targeted MR contrast agents, the series of the DO3A based multifunctional chelating agents with the variable length of the side chain has been synthesized. They serve as valuable multipurpose precursors for contrast agents based on gadolinium chelates in the design of (...) relaxometric MR probes. The presence of the amino group in the side chain of the macrocycle allows for conversion into various functional groups (aminophosponates, aminocarboxylates, etc.) or for conjugation with different biomolecules, dyes, and polymers. Choice of the functional groups depends on the.. (shrink)