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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.
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
Full Text: DOI
[1] Fibre-smallness: For all sets X, the class of C-objects on X is a set.
[2] H.Ćmiel, F.-V. Kuhlmann and K. Kuhlmann, A generic approach to measuring the strength of completeness/compactness of various types of spaces and ordered structures, to appear in Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, arXiv:1905.09930v2.
[3] W. Kubis and F.-V. Kuhlmann, Chain intersection closures, Topology Appl., 262 (2019), 11-19, arXiv:1810.05832v1. · Zbl 1468.54003
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[5] F.-V. Kuhlmann, K. Kuhlmann and M. Paulsen, The Caristi-Kirk fixed point theorem from the point of view of ball spaces, J. Fixed Point Theory Appl. 20 (3) (2018), Paper No. 107. · Zbl 1398.54075
[6] F.-V. Kuhlmann, K. Kuhlmann and F. Sonaallah, Coincidence point theorems for ball spaces and their applications, Ordered algebraic structures and related topics, Luminy, Contemporary Mathematics 697, 211-226, American Mathe-matical Society, Providence, 2017. · Zbl 1394.54024
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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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