Abstract
Topology has been shown to be definable in several cryptomorphically equivalent ways: by a neighborhood system, by a collection of open sets (be these given as a vector along the powerset or as a partial diagonal on it), by a collection of closed sets, or by a mapping to open kernels.
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Notes
- 1.
Georg Aumann (1906–1980) was a professor at TU München since 1960. Already in 1934/35 he visited the Institute for Advanced Studies in Princeton as a Rockefeller scholar. Some consider him as one of the more significant mathematicians of the first half of the twentieth century, not least because of his book Reelle Funktionen, [Aum69]. The first author has in 1968 been with him among those who formally founded the Mathematics unit of TUM—terminating its existence as an informal substructure of the old faculty of ‘Allgemeine Wissenschaften’.
- 2.
One has a rather firm feeling for negation; e.g. monotony when doubly negated. Do we have a corresponding feeling for “∕” and “∖” and how they operate together? Earlier denotations “” (once designed contrasting to “;”), “⋅ .”, and “. ⋅” (in diverging intention!) have provided some confusion as it has been reported already in [SS89, SS93].
References
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Schmidt, G., Winter, M. (2018). Closures and Their Aumann Contacts. In: Relational Topology. Lecture Notes in Mathematics, vol 2208. Springer, Cham. https://doi.org/10.1007/978-3-319-74451-3_7
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