A New Diagonal Separation and its Relations With the Hausdorff Property

Result code in 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>
Result on the web
<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>

Result language
angličtina
Original language name
A New Diagonal Separation and its Relations With the Hausdorff Property
Original language description
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 -> 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 -> M being frame homomorphisms (while one has such a characteristic of (sH) with weak homomorphisms, where meet-requirement is relaxed).
Czech name
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Czech description
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Type
J<sub>imp</sub> - 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
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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