Categorically-algebraic topology
نویسنده
چکیده
This talk aims at presenting a new way of approaching topological structures, induced by recent developments in the eld of lattice-valued topology, and deemed to incorporate in itself both crisp and many-valued settings. Based on category theory and universal algebra, the new framework is called categorically-algebraic (catalg) [9-12], to underline its motivating theories, on one hand, and to distinguish it from the currently dominating among the respective researchers point-set latticetheoretic (poslat) topology of S. E. Rodabaugh [7], on the other. At the bottom of the new approach lies a generalization of several aspects of the standard topological framework. Taking the case of classical topological spaces as an example, there are three main cornerstones in their theory. 1. The starting backward powerset operator, which can be represented as a
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