Frames of continuous functions

Wouter Van Den Haute; Mark Sioen; Wendy Lowen

doi:10.1016/j.topol.2019.106974

Frames of continuous functions

Wouter Van Den Haute, Mark Sioen, Wendy Lowen

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

In the standard approach to pointfree topology via frames/locales, a topological space is represented by its frame of open subsets. The aim of this note is to propose an alternative approach, by representing a topological space by a frame of continuous functions with values in what we call a topological frame. A prime example of such a familiar representation is the frame of lower semicontinuous [0,\infty]-valued functions on a topological space.

Original language	English
Article number	106974
Journal	Topology and its Applications
Volume	273
DOIs	https://doi.org/10.1016/j.topol.2019.106974
Publication status	Published - 15 Mar 2020

Bibliographical note

Funding Information:
Wendy Lowen acknowledges support of the European Union for the ERC Grant No. 257004-HHNcdMir, of the Research Foundation Flanders (FWO) under Grant No. G.0112.13N, and of the Russian Academic Excellence Project ‘5–100’. Mark Sioen thanks the Research Foundation Flanders (FWO) for support under the form of the grant “Krediet aan navorser” No. 1518317N.

Publisher Copyright:
© 2019 Elsevier B.V.

Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.

Access to Document

10.1016/j.topol.2019.106974

Cite this

@article{85e7c6bbea8c49f6b72480407b87939e,

title = "Frames of continuous functions",

abstract = "In the standard approach to pointfree topology via frames/locales, a topological space is represented by its frame of open subsets. The aim of this note is to propose an alternative approach, by representing a topological space by a frame of continuous functions with values in what we call a topological frame. A prime example of such a familiar representation is the frame of lower semicontinuous [0,\infty]-valued functions on a topological space.",

author = "{Van Den Haute}, Wouter and Mark Sioen and Wendy Lowen",

note = "Funding Information: Wendy Lowen acknowledges support of the European Union for the ERC Grant No. 257004-HHNcdMir, of the Research Foundation Flanders (FWO) under Grant No. G.0112.13N, and of the Russian Academic Excellence Project {\textquoteleft}5–100{\textquoteright}. Mark Sioen thanks the Research Foundation Flanders (FWO) for support under the form of the grant “Krediet aan navorser” No. 1518317N. Publisher Copyright: {\textcopyright} 2019 Elsevier B.V. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.",

year = "2020",

month = mar,

day = "15",

doi = "10.1016/j.topol.2019.106974",

language = "English",

volume = "273",

journal = "Topology and its Applications",

issn = "0166-8641",

publisher = "Elsevier",

}

TY - JOUR

T1 - Frames of continuous functions

AU - Van Den Haute, Wouter

AU - Sioen, Mark

AU - Lowen, Wendy

N1 - Funding Information: Wendy Lowen acknowledges support of the European Union for the ERC Grant No. 257004-HHNcdMir, of the Research Foundation Flanders (FWO) under Grant No. G.0112.13N, and of the Russian Academic Excellence Project ‘5–100’. Mark Sioen thanks the Research Foundation Flanders (FWO) for support under the form of the grant “Krediet aan navorser” No. 1518317N. Publisher Copyright: © 2019 Elsevier B.V. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.

PY - 2020/3/15

Y1 - 2020/3/15

N2 - In the standard approach to pointfree topology via frames/locales, a topological space is represented by its frame of open subsets. The aim of this note is to propose an alternative approach, by representing a topological space by a frame of continuous functions with values in what we call a topological frame. A prime example of such a familiar representation is the frame of lower semicontinuous [0,\infty]-valued functions on a topological space.

AB - In the standard approach to pointfree topology via frames/locales, a topological space is represented by its frame of open subsets. The aim of this note is to propose an alternative approach, by representing a topological space by a frame of continuous functions with values in what we call a topological frame. A prime example of such a familiar representation is the frame of lower semicontinuous [0,\infty]-valued functions on a topological space.

UR - http://www.scopus.com/inward/record.url?scp=85077149059&partnerID=8YFLogxK

U2 - 10.1016/j.topol.2019.106974

DO - 10.1016/j.topol.2019.106974

M3 - Article

VL - 273

JO - Topology and its Applications

JF - Topology and its Applications

SN - 0166-8641

M1 - 106974

ER -

Frames of continuous functions

Abstract

Bibliographical note

Access to Document

Other files and links

Fingerprint

Cite this