Generalized Open Mapping Theorem for X-Normed Spaces
- Authors: Comicheo A.B.1
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Affiliations:
- Department of Mathematics
- Issue: Vol 11, No 2 (2019)
- Pages: 135-150
- Section: Research Articles
- URL: https://journals.rcsi.science/2070-0466/article/view/201185
- DOI: https://doi.org/10.1134/S2070046619020043
- ID: 201185
Cite item
Abstract
The theory of X-normed spaces over non-Archimedean valued fields with valuations of higher rank was introduced by H. Ochsenius and W. H. Schikhof in [9] and further developed in [10–12, 16, 17] and [13]. In order to obtain results like the Open Mapping Theorem, the Closed Graph Theorem and the Uniform Boundedness Theorem, H. Ochsenius and W. H. Schikhof used 1st countability conditions in the value group of the based field. In this article the author develops a new tool to work with transfinite induction simplifying the techniques employed in X-normed spaces, thus accomplishing a Generalized Baire Category Theorem that allows the proof of an Open Mapping Theorem for X-normed spaces without restrictions on the value group of the based field. Additionally, some contributions to the theory of X-normed spaces are presented regarding quotient spaces.
About the authors
Angel Barria Comicheo
Department of Mathematics
Author for correspondence.
Email: angelbarriac@gmail.com
Canada, Winnipeg, Manitoba, R3T 2N2
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