# Uniformly $\mu $-continuous topologies on Köthe-Bochner spaces and Orlicz-Bochner spaces

Commentationes Mathematicae Universitatis Carolinae (1998)

- Volume: 39, Issue: 3, page 453-468
- ISSN: 0010-2628

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topFeledziak, Krzysztof. "Uniformly $\mu $-continuous topologies on Köthe-Bochner spaces and Orlicz-Bochner spaces." Commentationes Mathematicae Universitatis Carolinae 39.3 (1998): 453-468. <http://eudml.org/doc/248263>.

@article{Feledziak1998,

abstract = {Some class of locally solid topologies (called uniformly $\mu $-continuous) on 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 $\mathcal \{T\}^\varphi _I(X)$ on the Orlicz-Bochner space $L^\varphi (X)$ is a generalized mixed topology in the sense of P. Turpin (see [11, Chapter I]).},

author = {Feledziak, Krzysztof},

journal = {Commentationes Mathematicae Universitatis Carolinae},

keywords = {Orlicz spaces; Orlicz-Bochner spaces; Köthe-Bochner spaces; locally solid topologies; generalized mixed topologies; uniformly $\mu $-continuous topologies; inductive limit topologies; Köthe-Bochner spaces; Orlicz-Bochner spaces; locally solid topology; generalized mixed topology; inductive limit topology; uniformly -continuous topology},

language = {eng},

number = {3},

pages = {453-468},

publisher = {Charles University in Prague, Faculty of Mathematics and Physics},

title = {Uniformly $\mu $-continuous topologies on Köthe-Bochner spaces and Orlicz-Bochner spaces},

url = {http://eudml.org/doc/248263},

volume = {39},

year = {1998},

}

TY - JOUR

AU - Feledziak, Krzysztof

TI - Uniformly $\mu $-continuous topologies on Köthe-Bochner spaces and Orlicz-Bochner spaces

JO - Commentationes Mathematicae Universitatis Carolinae

PY - 1998

PB - Charles University in Prague, Faculty of Mathematics and Physics

VL - 39

IS - 3

SP - 453

EP - 468

AB - Some class of locally solid topologies (called uniformly $\mu $-continuous) on 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 $\mathcal {T}^\varphi _I(X)$ on the Orlicz-Bochner space $L^\varphi (X)$ is a generalized mixed topology in the sense of P. Turpin (see [11, Chapter I]).

LA - eng

KW - Orlicz spaces; Orlicz-Bochner spaces; Köthe-Bochner spaces; locally solid topologies; generalized mixed topologies; uniformly $\mu $-continuous topologies; inductive limit topologies; Köthe-Bochner spaces; Orlicz-Bochner spaces; locally solid topology; generalized mixed topology; inductive limit topology; uniformly -continuous topology

UR - http://eudml.org/doc/248263

ER -

## References

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