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Construction of ball spaces and the notion of continuity. (English) Zbl 1475.54001
The authors discuss the construction of new ball spaces through a set of theoretical operations on the balls. A definition of continuity for functions on ball spaces leads to the notion of quotient spaces. Further, they show the existence of products and coproducts and use this to derive a topological category associated with ball spaces. In the end, an open question is given.
MSC:
54A05 Topological spaces and generalizations (closure spaces, etc.)
54H25 Fixed-point and coincidence theorems (topological aspects)
12J15 Ordered fields
03E20 Other classical set theory (including functions, relations, and set algebra)
18B05 Categories of sets, characterizations
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[16] Katarzyna Kuhlmann Institute of Mathematics, ul. Wielkopolska 15, 70-451 Szczecin, Poland Katarzyna.Kuhlmann@usz.edu.pl Franz-Viktor Kuhlmann, Institute of Mathematics, ul. Wielkopolska 15, 70-451 Szczecin, Poland fvk@usz.edu.pl
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