based on a complete heyting algebra, we modify the definition oflattice-valued fuzzifying convergence space using fuzzy inclusionorder and construct in this way a cartesian-closed category, calledthe category of $l-$ordered fuzzifying convergence spaces, in whichthe category of $l-$fuzzifying topological spaces can be embedded.in addition, two new categories are introduced, which are called the...

We pose the problem of whether every FS-domain is a retract of abifinite domain purely in terms of quasi-uniform spaces. 6.1 The problem and its historyEver since domains were introduced by Dana Scott [Sco70] and Yuri Er-shov [Ers75], a question in the centre of interest was to find suitable cartesianclosed categories of domains and the quest for cartesian closed categories ...

We introduce the category NCSet consisting of neutrosophic crisp sets and morphisms between them. And we study NCSet in the sense of a topological universe and prove that it is Cartesian closed over Set, where Set denotes the category consisting of ordinary sets and ordinary mappings between them. 2010 AMS Classification: 03E72, 18B05

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...

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...