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On Immediate Extensions of Ultrametric Spaces

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Abstract

The purpose of this paper is to define immediate extensions of ultrametric spaces with a totally ordered value set. It will be proved that an ultrametric space (X, d) with value set F is maximal if and only if it is pseudocomplete, i. e. any pseudoconvergent sequence of (X, d) has a pseudolimit in X. Every ultrametric space will be shown to possess a maximal immediate extension, but its uniqueness can only be obtained within the more specific class of essential extensions.

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  1. Mathematisches Institut der Ludwig-Maximilians-Universität München, Theresienstraße 39, 80333, München, Deutschland, Germany

    Erwin Schörner

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  1. Erwin Schörner
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Schörner, E. On Immediate Extensions of Ultrametric Spaces. Results. Math. 29, 361–370 (1996). https://doi.org/10.1007/BF03322231

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  • DOI: https://doi.org/10.1007/BF03322231

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