Ultrametric spaces, valued and semivalued groups arising from the theory of shape

Cuchillo Ibáñez, EduardoAlonso Morón, ManuelRomero Ruiz Del Portal, Francisco2023-06-202023-06-202012978-84-695-4421-1https://hdl.handle.net/20.500.14352/45360In this paper we construct many generalizad ultrametrics in the sets of shape morphisms between topological spaes. We recognize a topology in these sets which is independen on the shape representation of the spaces. We construct valuations an semivaluations on groups of shape equivalences and on n-th shape groups. We also connect shape theory, for arbitrary topological spaces, with the algebraic theory of generalized ultrametric spaces developed by S. Priess-Crampe and P. Ribenboim among other authors.engUltrametric spaces, valued and semivalued groups arising from the theory of shapebook parthttp://cisne.sim.ucm.es/record=b3232194~S6*spiopen access514515.1Shape morphismsShape equivalencesShape groupsUltrametricsValuations and semivaluations on groupsGeometríaTopología1204 Geometría1210 Topología