The classical ring of quotients of $C_c(X)$

Papiya Bhattacharjee, Michelle L. Knox, Warren Wm. McGovern

Abstract

We construct the classical ring of quotients of the algebra of continuous real-valued functions with countable range. Our construction is a slight modification of the construction given in [M. Ghadermazi, O.A.S. Karamzadeh, and M. Namdari, On the functionally countable subalgebra of C(X), Rend. Sem. Mat. Univ. Padova, to appear]. Dowker's example shows that the two constructions can be different.

Keywords

ring of continuous functions; ring of quotients; zero-dimensional space.

Subject classification

54C40; 13B30.

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References

R. Engelking, General Topology, Sigma Ser. Pure Math. 6 (Heldermann Verlag, Berlin, 1989).

N. J. Fine, L. Gillman and J. Lambek, Rings of Quotients of Rings of Functions, Lecture Note Series ( McGill University Press, Montreal, 1966).

M. Ghadermazi, O. A. S. Karamzadeh and M. Namdari, On the functionally countable subalgebra of $C(X)$, Rend. Sem. Mat. Univ. Padova, to appear.

L. Gillman and M. Jerison, Rings of Continuous Functions, Graduate Texts in Mathematics, 43, (Springer Verlag, Berlin-Heidelberg-New York, 1976).

A. Hager, Cozero fields, Confer. Sem. Mat. Univ. Bari. 175 (1980), 1-23.

A. Hager, C. Kimber and W. Wm. McGovern, Unique a-closure for some l-groups of rational valued functions, Czech. Math. J. 55 (2005), 409-421.

(http://dx.doi.org/10.1007/s10587-005-0031-z)

M. Henriksen and R. G. Woods, Cozero complemented spaces; when the space of minimal prime ideals of a $C(X)$ is compact, Topology Appl. 141, no. 1-3 (2004), 147-170.

(http://dx.doi.org/10.1016/j.topol.2003.12.004)

M. L. Knox and W. Wm. McGovern, Rigid extensions of l-groups of continuous functions, Czech. Math. Journal 58 (133) (2008), 993-1014.

(http://dx.doi.org/10.1007/s10587-008-0064-1)

R. Levy and M. D. Rice, Normal $P$-spaces and the $G_delta$-topology, Colloq. Math. 44, no. 2 (1981), 227-240.

R. Levy and J. Shapiro, Rings of quotients of rings of functions, Topology Appl. 146/147 (2005), 253-265.

(http://dx.doi.org/10.1016/j.topol.2003.03.003)

A. Mysior, Two easy examples of zero-dimensional spaces, Proc. Amer. Math. Soc. 92, no. 4 (1984), 615-617.

M. Namdari and A. Veisi, Rings of quotients of the subalgebra of $C(X)$ consisting of functions with countable image, Inter. Math. Forum 7 (2012), 561-571.

J. Porter and R. G. Woods, Extensions and Absolutes of Hausdorff Spaces, (Springer-Verlag, New York, 1988).

(http://dx.doi.org/10.1007/978-1-4612-3712-9)

W. Rudin, Continuous functions on compact spaces without perfect subsets, Proc. Amer. Math. Soc. 8 (1957), 39-42.

(http://dx.doi.org/10.1090/S0002-9939-1957-0085475-7)

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1. On c-realcompact spaces
O.A.S. Karamzadeh, Z. Keshtkar
Quaestiones Mathematicae  vol: 41  issue: 8  first page: 1135  year: 2018  
doi: 10.2989/16073606.2018.1441919



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