On countable tightness and the Lindelöf property in non-Archimedean Banach spaces

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F18%3A00488913" target="_blank" >RIV/67985840:_____/18:00488913 - isvavai.cz</a>

Result on the web

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DOI - Digital Object Identifier

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Result language

angličtina

Original language name

On countable tightness and the Lindelöf property in non-Archimedean Banach spaces

Original language description

Let K be a non-archimedean valued field and let E be a non-archimedean Banach space over K. By E-w we denote the space E equipped with its weak topology and by E-w*(*) the dual space E* equipped with its weak* topology. Several results about countable tightness and the Lindelof property for E-w and E-w*(*) are provided. A key point is to prove that for a large class of infinite-dimensional polar Banach spaces E, countable tightness of E-w or E-w*(*) implies separability of K. As a consequence we obtain the following two characterizations of K : n(a) A non-archimedean valued field K is locally compact if and only if for every Banach space E over K the space E-w has countable tightness if and only if for every Banach space E over K the space E-w*(*) has the Lindelof property. n(b) A non-archimedean valued separable field K is spherically complete if and only if every Banach space E over K for which E-w has the Lindelof property must be separable if and only if every Banach space E over K for which E-w*(*) has countable tightness must be separable. Both results show how essentially different are non-archimedean counterparts from the 'classical' corresponding theorems for Banach spaces over the real or complex field.

Czech name

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Czech description

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Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

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OECD FORD branch

10101 - Pure mathematics

Project

<a href="/en/project/GF16-34860L" target="_blank" >GF16-34860L: Logic and Topology in Banach spaces</a><br>

Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2018

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Journal of Convex Analysis

ISSN

0944-6532

e-ISSN

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Volume of the periodical

25

Issue of the periodical within the volume

1

Country of publishing house

DE - GERMANY

Number of pages

19

Pages from-to

181-199

UT code for WoS article

000428115600011

EID of the result in the Scopus database

2-s2.0-85045912031