We present here "the" cartesian closed theory for real analytic mappings. It is based on the concept of real analytic curves in locally convex vector spaces. A mapping is real analytic, if it maps smooth curves to smooth curves and real analytic curves to real analytic curves. Under mild completeness conditions the second requirement can be replaced by: real analytic along aane lines. Enclosed ...

In our previous work [17] we have shown that for any ω-algebraic meet-cpo D, if all higher-order stable function spaces built from D are ω-algebraic, then D is finitary. This accomplishes the first of a possible, two-step process in solving the problem raised in [1, 2]: whether the category of stable bifinite domains of Amadio-Droste-Göbel [1, 6] is the largest cartesian closed full subcategory...

The main result of this paper may be stated as a construction of “almost representations” μn and μ̃n for the presheaves Obn and Õbn on the C-systems defined by locally cartesian closed universe categories with binary product structures and the study of the behavior of these “almost representations” with respect to the universe category functors. In addition, we study a number of constructions on...

We define and study the property of local diagonality for partial algebras and also a pair of related properties. We show that each of the three properties, together with idempotency, gives a cartesian closed initially structured subcategory of the category of all partial algebras of a given type. MSC 2000: 08A55, 08C05, 18D15

This paper presents two categories of effective continuous cpos. We define a new criterion on the basis of a cpo as to make the resulting category of consistently complete continuous cpos cartesian closed. We also generalise the definition of a complete set, used as a definition of effective bifinite domains in [HSH02], and investigate what closure results that can be obtained.

A setoid is a set together with a constructive representation of an equivalencerelation on it. Here, we give category theoretic support to the notion. Wefirst define a category Setoid and prove it is cartesian closed with coproducts.We then enrich it in the cartesian closed category Equiv of sets and classicalequivalence relations, extend the above results, and prove that Setoid...

We generalise Joyal’s notion of species of structures and develop their combinatorial calculus. In particular, we provide operations for their composition, addition, multiplication, pairing and projection, abstraction and evaluation, and differentiation; developing both the cartesian closed and linear structures of species.

The category TOP of topological spaces is not cartesian closed, but can be embedded into the cartesian closed category CONV of convergence spaces. It is well known that the category DCPO of dcpos and Scott continuous functions can be embedded into TOP, and so into CONV, by considering the Scott topology. We propose a di3erent, “cotopological” embedding of DCPO into CONV, which, in contrast to t...

We show that the cartesian closed category of compactly generated Hausdorff spaces is regular, but is neither exact, nor locally cartesian closed. In fact we find a coequalizer of an equivalence relation which is not stable under pullbacks.