Complexities and representations of F-Borel spaces

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F19%3A10401075" target="_blank" >RIV/00216208:11320/19:10401075 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/68407700:21230/19:00337954

Výsledek na webu

<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=VaY54Lsinq" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=VaY54Lsinq</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.4064/dm794-2-2019" target="_blank" >10.4064/dm794-2-2019</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Complexities and representations of F-Borel spaces

Popis výsledku v původním jazyce

We investigate the F-Borel complexity of topological spaces in their different compactifications. We provide a simple proof of the fact that a space can have arbitrarily many different complexities in different compactifications. We also develop a theory of representations of F-Borel sets, and show how to apply this theory to prove that the complexity of hereditarily Lindelof spaces is absolute (that is, the same in every compactification). We use these representations to characterize the complexities attainable by a specific class of topological spaces. This provides an alternative proof of the first result, and implies the existence of a space with non-absolute additive complexity. We discuss the method used by Talagrand to construct the first example of a space with non-absolute complexity, hopefully providing an explanation which is more accessible than the original one. We also discuss the relation between complexity and local complexity, and show how to construct amalgamation-like compactifications.

Název v anglickém jazyce

Complexities and representations of F-Borel spaces

Popis výsledku anglicky

We investigate the F-Borel complexity of topological spaces in their different compactifications. We provide a simple proof of the fact that a space can have arbitrarily many different complexities in different compactifications. We also develop a theory of representations of F-Borel sets, and show how to apply this theory to prove that the complexity of hereditarily Lindelof spaces is absolute (that is, the same in every compactification). We use these representations to characterize the complexities attainable by a specific class of topological spaces. This provides an alternative proof of the first result, and implies the existence of a space with non-absolute additive complexity. We discuss the method used by Talagrand to construct the first example of a space with non-absolute complexity, hopefully providing an explanation which is more accessible than the original one. We also discuss the relation between complexity and local complexity, and show how to construct amalgamation-like compactifications.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

Výsledek vznikl pri realizaci vícero projektů. Více informací v záložce Projekty.

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2019

Kód důvěrnosti údajů

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

Název periodika

Dissertationes Mathematicae

ISSN

0012-3862

e-ISSN

—

Svazek periodika

540

Číslo periodika v rámci svazku

540

Stát vydavatele periodika

PL - Polská republika

Počet stran výsledku

69

Strana od-do

1-69

Kód UT WoS článku

000476629800001

EID výsledku v databázi Scopus

2-s2.0-85069843567