منابع مشابه
Separation Classes of Equilogical Spaces
The category TOP of topological spaces is not cartesian closed, but can be embedded into the cartesian closed category ASSM of assemblies over algebraic lattices, which is a generalisation of Scott's category EQU of equilogical spaces. In this paper, we identify cartesian closed subcategories of assemblies which correspond to well-known separation properties of topology: T 0 ,
متن کاملEquilogical spaces
It is well known that one can build models of full higher-order dependent type theory (also called the calculus of constructions) using partial equivalence relations (PERs) and assemblies over a partial combinatory algebra (PCA). But the idea of categories of PERs and ERs (total equivalence relations) can be applied to other structures as well. In particular, we can easily define the category o...
متن کاملEquilogical spaces and filter spaces
The paper is about the comparison between (apparently) different cartesian closed extensions of the category of topological spaces. Since topological spaces do not in general allow formation of function spaces, the problem of determining suitable categories with such a property—and nicely related to that of topological spaces—was studied from many different perspectives: general topology, funct...
متن کاملEquilogical Spaces, Homology and Noncommutative Geometry ( * )
After introducing singular homology for D. Scott's equilogical spaces [Sc], we show how these structures can express 'formal quotients' of topological spaces, which do not exist as ordinary spaces and are related with well-known noncommutative C*-algebras. This study also uses a wider notion of local maps between equilogical spaces, which might be of interest for the general theory of the latte...
متن کاملInjective Convergence Spaces and Equilogical Spaces via Pretopological Spaces
Sierpinski space Ω is injective in the category Top of topological spaces, but not in any of the larger cartesian closed categories Conv of convergence spaces and Equ of equilogical spaces. We show that this negative result extends to all sub-cccs of Equ and Conv that are closed under subspaces and contain Top. On the other hand, we study the category PrTop of pretopological spaces that lies in...
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ژورنال
عنوان ژورنال: Electronic Notes in Theoretical Computer Science
سال: 1999
ISSN: 1571-0661
DOI: 10.1016/s1571-0661(04)80079-3