Algebras and spaces of dense constancies

Angelo Bella; Jorge Martinez; Scott D. Woodward

Czechoslovak Mathematical Journal (2001)

  • Volume: 51, Issue: 3, page 449-461
  • ISSN: 0011-4642

Abstract

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A DC-space (or space of dense constancies) is a Tychonoff space X such that for each f ∈ C ( X ) there is a family of open sets { U i i ∈ I } , the union of which is dense in X , such that f , restricted to each U i , is constant. A number of characterizations of DC-spaces are given, which lead to an algebraic generalization of the concept, which, in turn, permits analysis of DC-spaces in the language of archimedean f -algebras. One is led naturally to the notion of an almost DC-space (in which the densely constant functions are dense), and it is shown that all metrizable spaces have this property.

How to cite

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Bella, Angelo, Martinez, Jorge, and Woodward, Scott D.. "Algebras and spaces of dense constancies." Czechoslovak Mathematical Journal 51.3 (2001): 449-461. <http://eudml.org/doc/30647>.

@article{Bella2001,
abstract = {A DC-space (or space of dense constancies) is a Tychonoff space $X$ such that for each $f\in C(X)$ there is a family of open sets $\lbrace U_i\: i\in I\rbrace $, the union of which is dense in $X$, such that $f$, restricted to each $U_i$, is constant. A number of characterizations of DC-spaces are given, which lead to an algebraic generalization of the concept, which, in turn, permits analysis of DC-spaces in the language of archimedean $f$-algebras. One is led naturally to the notion of an almost DC-space (in which the densely constant functions are dense), and it is shown that all metrizable spaces have this property.},
author = {Bella, Angelo, Martinez, Jorge, Woodward, Scott D.},
journal = {Czechoslovak Mathematical Journal},
keywords = {space and algebra of dense constancy; $c$-spectrum; space and algebra of dense constancy; -spectrum},
language = {eng},
number = {3},
pages = {449-461},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Algebras and spaces of dense constancies},
url = {http://eudml.org/doc/30647},
volume = {51},
year = {2001},
}

TY - JOUR
AU - Bella, Angelo
AU - Martinez, Jorge
AU - Woodward, Scott D.
TI - Algebras and spaces of dense constancies
JO - Czechoslovak Mathematical Journal
PY - 2001
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 51
IS - 3
SP - 449
EP - 461
AB - A DC-space (or space of dense constancies) is a Tychonoff space $X$ such that for each $f\in C(X)$ there is a family of open sets $\lbrace U_i\: i\in I\rbrace $, the union of which is dense in $X$, such that $f$, restricted to each $U_i$, is constant. A number of characterizations of DC-spaces are given, which lead to an algebraic generalization of the concept, which, in turn, permits analysis of DC-spaces in the language of archimedean $f$-algebras. One is led naturally to the notion of an almost DC-space (in which the densely constant functions are dense), and it is shown that all metrizable spaces have this property.
LA - eng
KW - space and algebra of dense constancy; $c$-spectrum; space and algebra of dense constancy; -spectrum
UR - http://eudml.org/doc/30647
ER -

References

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