Autor: Watson, Saleem - Katalog OPAC zbiorów

Skocz do pozycji: 1.

Tytuł:: Structure spaces for rings of continuous functions with applications to realcompactifications
Autorzy:: Redlin, Lothar
Watson, Saleem
Powiązania:: https://bibliotekanauki.pl/articles/1205448.pdf
Data publikacji:: 1997
Wydawca:: Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:: ring of continuous functions
maximal ideal
ultrafilter
realcompactification
Opis:: Let X be a completely regular space and let A(X) be a ring of continuous real-valued functions on X which is closed under local bounded inversion. We show that the structure space of A(X) is homeomorphic to a quotient of the Stone-Čech compactification of X. We use this result to show that any realcompactification of X is homeomorphic to a subspace of the structure space of some ring of continuous functions A(X).
Źródło:: Fundamenta Mathematicae; 1997, 152, 2; 151-163
0016-2736
Pojawia się w:: Fundamenta Mathematicae
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 2.

Artykuł

Skocz do pozycji: 3.

Tytuł:: Correspondences between ideals and $z$-filters for rings of continuous functions between $C^∗$ and $C$
Autorzy:: Panman, Phyllis
Sack, Joshua
Watson, Saleem
Powiązania:: https://bibliotekanauki.pl/articles/745481.pdf
Data publikacji:: 2012
Wydawca:: Polskie Towarzystwo Matematyczne
Tematy:: Rings of continuous functions
Ideals
$z$-filters
Kernel
Hull
Opis:: Let $X$ be a completely regular topological space. Let $A(X)$ be a ring of continuous functions between $C^∗(X)$ and $C(X)$, that is, $C^∗(X) \subset A(X) \subset C(X)$. In [9], a correspondence $\mathcal{Z}_A$ between ideals of $A(X)$ and $z$-filters on $X$ is defined. Here we show that $\mathcal{Z}_A$ extends the well-known correspondence for $C^∗(X)$ to all rings $A(X)$. We define a new correspondence $\mathcal{Z}_A$ and show that it extends the well-known correspondence for $C(X)$ to all rings $A(X)$. We give a formula that relates the two correspondences. We use properties of $\mathcal{Z}_A$ and $\mathcal{Z}_A$ to characterize $C^∗(X)$ and $C(X)$ among all rings $A(X)$. We show that $\mathcal{Z}_A$ defines a one-one correspondence between maximal ideals in $A(X)$ and the $z$-ultrafilters in $X$.
Źródło:: Commentationes Mathematicae; 2012, 52, 1
0373-8299
Pojawia się w:: Commentationes Mathematicae
Dostawca treści:: Biblioteka Nauki

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