Journal of the
Korean Mathematical Society
JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

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J. Korean Math. Soc. 2009; 46(6): 1233-1242

Printed November 1, 2009

https://doi.org/10.4134/JKMS.2009.46.6.1233

Copyright © The Korean Mathematical Society.

The separable quotient problem for $(LF)_{tv}$-spaces

Wies{\l}aw {\'S}liwa

A. Mickiewicz University

Abstract

In 1981 S. A. Saxon and P. P. Narayanaswami ([10]) showed that every $(LF)$-space has an infinite dimensional separable quotient. In this note we prove that this fails for $(LF)_{tv}$-spaces. We construct a wide class of $(LF)_{tv}$-spaces, which have no infinite dimensional separable quotient.

Keywords: $F$-spaces, $(LF)_{tv}$-spaces, separable quotients

MSC numbers: 46A16

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