A New Diagonal Separation and its Relations With the Hausdorff Property

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F22%3A10455255" target="_blank" >RIV/00216208:11320/22:10455255 - isvavai.cz</a>

Výsledek na webu

<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=8WXrJrZXj1" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=8WXrJrZXj1</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s10485-021-09655-9" target="_blank" >10.1007/s10485-021-09655-9</a>

Jazyk výsledku

angličtina

Název v původním jazyce

A New Diagonal Separation and its Relations With the Hausdorff Property

Popis výsledku v původním jazyce

Let P be a property of subobjects relevant in a category C. An object X is an element of C is P-separated if the diagonal in X x X has P; thus e.g. closedness in the category of topological spaces (resp. locales) induces the Hausdorff (resp. strong Hausdorff) axiom. In this paper we study the locales (frames) in which the diagonal is fitted (i.e., an intersection of open sublocales-we speak about F-separated locales). Recall that a locale is fit if each of its sublocales is fitted. Since this property is inherited by products and sublocales, fitness implies (Fsep) which is shown to be strictly weaker (one of the results of this paper). We show that (Fsep) is in a parallel with the strong Hausdorff axiom (sH): (1) it is characterized by a Dowker-Strauss type property of the combinatorial structure of the systems of frame homomorphisms L -&gt; M (and therefore, in particular, it implies (T-U) for analogous reasons like (sH) does), and (2) in a certain duality with (sH) it is characterized in L by all almost homomorphisms (frame homomorphisms with slightly relaxed join-requirement) L -&gt; M being frame homomorphisms (while one has such a characteristic of (sH) with weak homomorphisms, where meet-requirement is relaxed).

Název v anglickém jazyce

A New Diagonal Separation and its Relations With the Hausdorff Property

Popis výsledku anglicky

Let P be a property of subobjects relevant in a category C. An object X is an element of C is P-separated if the diagonal in X x X has P; thus e.g. closedness in the category of topological spaces (resp. locales) induces the Hausdorff (resp. strong Hausdorff) axiom. In this paper we study the locales (frames) in which the diagonal is fitted (i.e., an intersection of open sublocales-we speak about F-separated locales). Recall that a locale is fit if each of its sublocales is fitted. Since this property is inherited by products and sublocales, fitness implies (Fsep) which is shown to be strictly weaker (one of the results of this paper). We show that (Fsep) is in a parallel with the strong Hausdorff axiom (sH): (1) it is characterized by a Dowker-Strauss type property of the combinatorial structure of the systems of frame homomorphisms L -&gt; M (and therefore, in particular, it implies (T-U) for analogous reasons like (sH) does), and (2) in a certain duality with (sH) it is characterized in L by all almost homomorphisms (frame homomorphisms with slightly relaxed join-requirement) L -&gt; M being frame homomorphisms (while one has such a characteristic of (sH) with weak homomorphisms, where meet-requirement is relaxed).

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

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

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2022

Kód důvěrnosti údajů

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

Název periodika

Applied Categorical Structures

ISSN

0927-2852

e-ISSN

1572-9095

Svazek periodika

30

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

17

Strana od-do

247-263

Kód UT WoS článku

000677932800001

EID výsledku v databázi Scopus

2-s2.0-85111520007