Geodesic
Uniformly $\mu$-continuous topologies on Köthe-Bochner spaces and Orlicz-Bochner spaces
Commentationes Mathematicae Universitatis Carolinae, Tome 39 (1998) no. 3, pp. 453-468.

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Some class of locally solid topologies (called uniformly $\mu$-continuous) on \linebreak Köthe-Bochner spaces that are continuous with respect to some natural two-norm convergence are introduced and studied. A characterization of uniformly $\mu$-continuous topologies in terms of some family of pseudonorms is given. The finest uniformly $\mu$-continuous topology $\Cal T^\varphi_I(X)$ on the Orlicz-Bochner space $L^\varphi(X)$ is a generalized mixed topology in the sense of P. Turpin (see [11, Chapter I]).
Classification : 46A70, 46E30, 46E40
Keywords: Orlicz spaces; Orlicz-Bochner spaces; Köthe-Bochner spaces; locally solid topologies; generalized mixed topologies; uniformly $\mu$-continuous topologies; inductive limit topologies 
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     title = {Uniformly $\mu$-continuous topologies on {K\"othe-Bochner} spaces and {Orlicz-Bochner} spaces},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {453--468},
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     number = {3},
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Feledziak, Krzysztof. Uniformly $\mu$-continuous topologies on Köthe-Bochner spaces and Orlicz-Bochner spaces. Commentationes Mathematicae Universitatis Carolinae, Tome 39 (1998) no. 3, pp. 453-468. http://geodesic.mathdoc.fr/item/CMUC_1998__39_3_a2/