Projective and inductive generations of relator spaces. (English) Zbl 0695.54021
Given a set X and a non-void family \({\mathcal R}\) of reflexive relations on X, the author calls \({\mathcal R}^ a \)relator on X and defines the relator space X(\({\mathcal R})\) to be the pair (X,\({\mathcal R})\). Then he/she calls a relation f from one relator space Y(S) to another one Z(\({\mathcal T})\) mildly continuous if \(f^{-1}\circ T\circ f\in {\mathcal S}\) for all \(T\in {\mathcal T}\). These spaces and relations generalize uniformity: elsewhere, the author proposed them as ‘the most suitable’ for topology and analysis [Acta Math. Hung. 50, 177-201 (1987; Zbl 0643.54033)]. Here the author explicitly constructs the extremal objects in this category (both projective and inductive ones), and provides some illustrative examples.
Reviewer: M.Schroder
MSC:
| 54E15 | Uniform structures and generalizations |
| 54B30 | Categorical methods in general topology |
| 18B10 | Categories of spans/cospans, relations, or partial maps |
Citations:
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