Construction of ball spaces and the notion of continuity

Authors

  • René Bartsch A.-v.-Humboldt-Gymnasium
  • Katarzyna Kuhlmann University of Stettin
  • Franz-Viktor Kuhlmann University of Szczecin

DOI:

https://doi.org/10.53733/157

Abstract

Spherically complete ball spaces provide a simple framework for the encoding of completeness properties of various spaces and ordered structures. This allows to prove generic versions of theorems that work with these completeness properties, such as fixed point theorems and related results. For the purpose of applying the generic theorems, it is important to have methods for the construction of new spherically complete ball spaces from existing ones. Given various ball spaces on the same underlying set, we discuss the construction of new ball spaces through set theoretic operations on the balls. A definition of continuity for functions on ball spaces leads to the notion of quotient spaces. Further, we show the existence of products and coproducts and use this to derive a topological category associated with ball spaces.

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Author Biographies

René Bartsch, A.-v.-Humboldt-Gymnasium

A.-v.-Humboldt-Gymnasium,
Makarenkostr. 54,
17491 Greifswald,
Germany

Katarzyna Kuhlmann, University of Stettin

Institute of Mathematics,
ul. Wielkopolska 15,
70-451 Szczecin,
Poland

Franz-Viktor Kuhlmann, University of Szczecin

Institute of Mathematics,
ul. Wielkopolska 15,
70-451 Szczecin,
Poland

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Published

12-08-2021

How to Cite

Bartsch, R., Kuhlmann, K., & Kuhlmann, F.-V. (2021). Construction of ball spaces and the notion of continuity. New Zealand Journal of Mathematics, 51, 49–64. https://doi.org/10.53733/157

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Articles