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.
Wies{\l}aw {\'S}liwa
A. Mickiewicz University
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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