Group-valued continuous functions with the topology of pointwise convergence

Result code in 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>
Result on the web
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DOI - Digital Object Identifier
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Result language
angličtina
Original language name
Group-valued continuous functions with the topology of pointwise convergence
Original language description
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
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Publication year
2010
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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