# 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

## Access Full Article

top## Abstract

top## How to cite

topBella, 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

top- 10.4153/CJM-1965-044-7, Canad. J. Math. 17 (1965), 434–448. (1965) Zbl0134.27101MR0174600DOI10.4153/CJM-1965-044-7
- Lattice-ordered groups. An introduction, Reidel Texts in the Math. Sciences, Kluwer, Dordrecht, 1988. (1988) MR0937703
- 10.1007/BF01220051, Arch. Math. 16 (1965), 414–420. (1965) Zbl0135.07901MR0199214DOI10.1007/BF01220051
- 10.1016/0166-8641(96)00026-0, Topology Appl. 72 (1996), 259–271. (1996) MR1406312DOI10.1016/0166-8641(96)00026-0
- Groupes et Anneaux Réticulés. LNM, Vol. 608, Springer-Verlag, Berlin-Heidelberg-New York, 1977. (1977) MR0552653
- 10.1016/1385-7258(76)90000-7, Indag. Math. 38 (1976), 1–7. (1976) Zbl0329.06013MR0401581DOI10.1016/1385-7258(76)90000-7
- Rings of Continuous Functions. GTM Vol. 43, Springer-Verlag, Berlin-Heidelberg-New York, 1976. (1976) MR0407579
- Minimal covers of topological spaces, Ann. New York Acad. Sci.; Papers on general topology and related category theory and topological algebra Alg. Vol. 552 (1989), 44–59. (1989) Zbl0881.54025MR1020773
- Lectures on Rings and Modules, Blaisdell Publ. Co., Waltham, 1966. (1966) Zbl0143.26403MR0419493
- 10.1007/BF01190704, Algebra Universalis 33 (1995), 355–369. (1995) MR1322778DOI10.1007/BF01190704
- 10.1007/BF01197178, Algebra Universalis 35 (1996), 333–341. (1996) MR1387909DOI10.1007/BF01197178
- Extensions and Absolutes of Hausdorff Spaces, Springer-Verlag, Berlin-Heidelberg-New York, 1988. (1988) MR0918341
- On quotient rings, Osaka Math. J. 8 (1956), 1–18. (1956) Zbl0070.26601MR0078966

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.