Notes on sublocales and dissolution

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F24%3A10493602" target="_blank" >RIV/00216208:11320/24:10493602 - isvavai.cz</a>

Result on the web

<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=LK0keaULhq" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=LK0keaULhq</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.2989/16073606.2024.2351184" target="_blank" >10.2989/16073606.2024.2351184</a>

Result language

angličtina

Original language name

Notes on sublocales and dissolution

Original language description

The dissolution (introduced by Isbell in [3], discussed by Johnstone in [5] and later exploited by Plewe in [12, 13]) is here viewed as the relation of the geometry of L with that of the more dispersed T(L) = S(L)op mediated by the natural embedding and its adjoint localic map gamma L: T(L) -&gt; L. The associated image-preimage adjunction (gamma L)-1 [-] &amp; dashv; gamma L [-] between the frames T(L) and TT(L) is shown to coincide with the adjunction cT(L) &amp; dashv; gamma T(L) of the second step of the assembly (tower) of L. This helps to explain the role of T(L) = S(L)op as an &quot;almost discrete lift&quot; (sometimes used as a sort of model of the classical discrete lift DL -&gt; L) as a dispersion going halfway to Booleanness. Consequent use of the concrete sublocales technique simplifies the reasoning. We illustrate it on the celebrated Plewe&apos;s theorem on ultranormality (and ultraparacompactness) of S(L) which becomes (we hope) substantially more transparent.

Czech name

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Czech description

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Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

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OECD FORD branch

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Project

—

Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2024

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Quaestiones Mathematicae

ISSN

1607-3606

e-ISSN

1727-933X

Volume of the periodical

47

Issue of the periodical within the volume

10

Country of publishing house

ZA - SOUTH AFRICA

Number of pages

15

Pages from-to

2053-2067

UT code for WoS article

001223899200001

EID of the result in the Scopus database

2-s2.0-85193051765