Description of quotient algebras in function algebras containing continuous unbounded functions

Mati Abel; Jorma Arhippainen; Jukka Kauppi

Open Mathematics (2012)

  • Volume: 10, Issue: 3, page 1060-1066
  • ISSN: 2391-5455

Abstract

top
Let X be a completely regular Hausdorff space, 𝔖 a cover of X, and C b ( X , 𝕂 ; 𝔖 ) the algebra of all 𝕂 -valued continuous functions on X which are bounded on every S 𝔖 . A description of quotient algebras of C b ( X , 𝕂 ; 𝔖 ) is given with respect to the topologies of uniform and strict convergence on the elements of 𝔖 .

How to cite

top

Mati Abel, Jorma Arhippainen, and Jukka Kauppi. "Description of quotient algebras in function algebras containing continuous unbounded functions." Open Mathematics 10.3 (2012): 1060-1066. <http://eudml.org/doc/269330>.

@article{MatiAbel2012,
abstract = {Let X be a completely regular Hausdorff space, \[\mathfrak \{S\}\] a cover of X, and \[C\_b (X,\mathbb \{K\};\mathfrak \{S\})\] the algebra of all \[\mathbb \{K\}\] -valued continuous functions on X which are bounded on every \[S \in \mathfrak \{S\}\] . A description of quotient algebras of \[C\_b (X,\mathbb \{K\};\mathfrak \{S\})\] is given with respect to the topologies of uniform and strict convergence on the elements of \[\mathfrak \{S\}\] .},
author = {Mati Abel, Jorma Arhippainen, Jukka Kauppi},
journal = {Open Mathematics},
keywords = {Function algebras; Quotient algebras; Cover; Uniform topology; Strict topology; function algebras; quotient algebras; cover; uniform topology; strict topology},
language = {eng},
number = {3},
pages = {1060-1066},
title = {Description of quotient algebras in function algebras containing continuous unbounded functions},
url = {http://eudml.org/doc/269330},
volume = {10},
year = {2012},
}

TY - JOUR
AU - Mati Abel
AU - Jorma Arhippainen
AU - Jukka Kauppi
TI - Description of quotient algebras in function algebras containing continuous unbounded functions
JO - Open Mathematics
PY - 2012
VL - 10
IS - 3
SP - 1060
EP - 1066
AB - Let X be a completely regular Hausdorff space, \[\mathfrak {S}\] a cover of X, and \[C_b (X,\mathbb {K};\mathfrak {S})\] the algebra of all \[\mathbb {K}\] -valued continuous functions on X which are bounded on every \[S \in \mathfrak {S}\] . A description of quotient algebras of \[C_b (X,\mathbb {K};\mathfrak {S})\] is given with respect to the topologies of uniform and strict convergence on the elements of \[\mathfrak {S}\] .
LA - eng
KW - Function algebras; Quotient algebras; Cover; Uniform topology; Strict topology; function algebras; quotient algebras; cover; uniform topology; strict topology
UR - http://eudml.org/doc/269330
ER -

References

top
  1. [1] Abel M., Extensions of topological spaces depending on covering, Eesti NSV Tead. Akad. Toimetised Füüs.-Mat., 1981, 30(4), 326–332 (in Russian) Zbl0478.54020
  2. [2] Abel M., The extensions of topological spaces depending on cover and its applications, In: General Topology and its Relations to Modern Analysis and Algebra, 5, The Fifth Prague Topological Symposium, Prague, August 24–28, 1981, Sigma Ser. Pure Math., 3, Heldermann, Berlin, 1983, 6–8 
  3. [3] Abel M., Arhippainen J., Kauppi J., Stone-Weierstrass type theorems for algebras containing continuous unbounded functions, Sci. Math. Jpn., 2010, 71(1), 1–10 Zbl1198.46025
  4. [4] Abel M., Arhippainen J., Kauppi J., Description of closed ideals in function algebras containing continuous unbounded functions, Mediterr. J. Math., 2010, 7(3), 271–282 http://dx.doi.org/10.1007/s00009-010-0035-2 Zbl1211.46055
  5. [5] Arhippainen J., On locally A-convex function algebras, In: General Topological Algebras, Tartu, October 4–7, 1999, Math. Stud. (Tartu), Est. Math. Soc. Tartu, 1, Estonian Mathematical Society, Tartu, 2001, 37–41 Zbl1029.46067
  6. [6] Arhippainen J., Kauppi J., Generalization of the topological algebra (C b(X); β), Studia Math., 2009, 191(3), 247–262 http://dx.doi.org/10.4064/sm191-3-6 Zbl1176.46050
  7. [7] Gillman L., Jerison M., Rings of continuous functions, The University Series in Higher Mathematics, Van Nostrand, Princeton-Toronto-London-New York, 1960 Zbl0093.30001
  8. [8] Willard S., General Topology, Addison-Wesley, Reading-London-Don Mills, 1970 

NotesEmbed ?

top

You must be logged in to post comments.

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

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.