Long chains of dense subspaces in Banach spaces

It is proved that every infinite-dimensional Banach space X of cardinality m admits both a strictly descending chain and a strictly ascending chain of dense linear subspaces of length m.

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Publication Details

Journal
Open Journal of Mathematical Analysis
Published
2025-10-16
DOI
https://doi.org/10.30538/psrp-oma2025.0173
Primary Topic
Advanced Banach Space Theory
Type
article
Field-Weighted Citation Impact
0.00
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article

Long chains of dense subspaces in Banach spaces

Sidney A. Morris
Open Journal of Mathematical Analysis
Advanced Banach Space Theory
article

Long chains of dense subspaces in Banach spaces

Sidney A. Morris
article en

Abstract

It is proved that every infinite-dimensional Banach space X of cardinality m admits both a strictly descending chain and a strictly ascending chain of dense linear subspaces of length m.

Open Journal of Mathematical AnalysisVol. 9(2)
Openalex Percentile: Top 64%
Advanced Banach Space Theory
DOIOpen Access PDFOpenAlex
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