Appia: formalization of its topology assignment droblem

A complete formalization of constructive topology

Looking for a complete formalization of constructive topology we analyzed the structure of the subsets of a Heyting algebra which correspond to the concrete closed and open sets of a topological space over its formal points. After this has been done, the rules for a formalization of constructive topology, which is both predicative and complete, are unveiled.

APPIA - GULP - PRODE 20001 Introdu

Categorically-algebraic topology and its applications

This paper introduces a new approach to topology, based on category theory and universal algebra, and called categorically-algebraic (catalg) topology. It incorporates the most important settings of lattice-valued topology, including poslat topology of S.~E.~Rodabaugh, $(L,M)$-fuzzy topology of T.~Kubiak and A.~v{S}ostak, and $M$-fuzzy topology on $L$-fuzzy sets of C.~Guido. Moreover, its respe...

Computational Topology

The authors of this article believe there is or should be a research area appropriately referred to as computa tional topology Its agenda includes the identi cation and formalization of topological questions in computer applications and the study of algorithms for topolog ical problems It is hoped this article can contribute to the creation of a computational branch of topology with a unifying ...

Appia - Gulp - Prode