Group-valued continuous functions with the topology of pointwise convergence

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F44555601%3A13440%2F10%3A00005948" target="_blank" >RIV/44555601:13440/10:00005948 - isvavai.cz</a>

Výsledek na webu

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DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

Group-valued continuous functions with the topology of pointwise convergence

Popis výsledku v původním jazyce

Let G be a topological group with the identity element e Given a space X, we denote by COX G) the group of all continuous functions from X to G endowed with the topology of pointwise convergence. and we say that X is (a) G-regular if, for each closed setF subset of X and every point x is an element of X F, there exist f is an element of C-p(X G) and g is an element of G {e} such that f(x) = g and f (F} subset of {e}, (b) G* -regular provided that there exists g is an element of G {e} such that, for each closed set F subset of X and every point x is an element of X F, one can find f is an element of C-p(X G) With f (x) - g and f (F) subset of {e} Spaces X and Y are G-equivalent provided that the topological groups C-p (X, G) and C-p(Y G) are topologically isomorphic. We investigate which topological properties are preserved by G-equivalence, with a special emphasis being placed on characterizing topological properties of X in terms of those of C-p(X,G) Since -equivalence coinci

Název v anglickém jazyce

Group-valued continuous functions with the topology of pointwise convergence

Popis výsledku anglicky

Let G be a topological group with the identity element e Given a space X, we denote by COX G) the group of all continuous functions from X to G endowed with the topology of pointwise convergence. and we say that X is (a) G-regular if, for each closed setF subset of X and every point x is an element of X F, there exist f is an element of C-p(X G) and g is an element of G {e} such that f(x) = g and f (F} subset of {e}, (b) G* -regular provided that there exists g is an element of G {e} such that, for each closed set F subset of X and every point x is an element of X F, one can find f is an element of C-p(X G) With f (x) - g and f (F) subset of {e} Spaces X and Y are G-equivalent provided that the topological groups C-p (X, G) and C-p(Y G) are topologically isomorphic. We investigate which topological properties are preserved by G-equivalence, with a special emphasis being placed on characterizing topological properties of X in terms of those of C-p(X,G) Since -equivalence coinci

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

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Návaznosti

S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2010

Kód důvěrnosti údajů

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

Název periodika

Topology and its Applications

ISSN

0166-8641

e-ISSN

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Svazek periodika

157

Číslo periodika v rámci svazku

8

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

23

Strana od-do

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Kód UT WoS článku

000277677500028

EID výsledku v databázi Scopus

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