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

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

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Bhattacharjee, P.; Knox, ML.; Mcgovern, WW. (2014). The classical ring of quotients of $C_c(X)$. Applied General Topology. 15(2):147-154. https://doi.org/10.4995/agt.2014.3181

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Título: The classical ring of quotients of $C_c(X)$
Autor: Bhattacharjee, Papiya Knox, Michelle L. McGovern, Warren Wm.
Fecha difusión:
Resumen:
[EN] 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. ...[+]
Palabras clave: Ring of continuous functions , Ring of quotients , Zero-dimensional space
Derechos de uso: Reconocimiento - No comercial - Sin obra derivada (by-nc-nd)
Fuente:
Applied General Topology. (issn: 1576-9402 ) (eissn: 1989-4147 )
DOI: 10.4995/agt.2014.3181
Editorial:
Editorial Universitat Politècnica de València
Versión del editor: https://doi.org/10.4995/agt.2014.3181
Tipo: Artículo

References

Hager, A. W., Kimber, C. M., & McGovern, W. W. (2005). Unique a-closure for some ℓ-groups of rational valued functions. Czechoslovak Mathematical Journal, 55(2), 409-421. doi:10.1007/s10587-005-0031-z

Henriksen, M., & Woods, R. G. (2004). Cozero complemented spaces; when the space of minimal prime ideals of a C(X) is compact. Topology and its Applications, 141(1-3), 147-170. doi:10.1016/j.topol.2003.12.004

Knox, M. L., & McGovern, W. W. (2008). Rigid extensions of ℓ-groups of continuous functions. Czechoslovak Mathematical Journal, 58(4), 993-1014. doi:10.1007/s10587-008-0064-1 [+]
Hager, A. W., Kimber, C. M., & McGovern, W. W. (2005). Unique a-closure for some ℓ-groups of rational valued functions. Czechoslovak Mathematical Journal, 55(2), 409-421. doi:10.1007/s10587-005-0031-z

Henriksen, M., & Woods, R. G. (2004). Cozero complemented spaces; when the space of minimal prime ideals of a C(X) is compact. Topology and its Applications, 141(1-3), 147-170. doi:10.1016/j.topol.2003.12.004

Knox, M. L., & McGovern, W. W. (2008). Rigid extensions of ℓ-groups of continuous functions. Czechoslovak Mathematical Journal, 58(4), 993-1014. doi: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.

Levy, R., & Shapiro, J. (2005). Rings of quotients of rings of functions. Topology and its Applications, 146-147, 253-265. doi: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.

Porter, J. R., & Woods, R. G. (1988). Extensions and Absolutes of Hausdorff Spaces. doi:10.1007/978-1-4612-3712-9

Rudin, W. (1957). Continuous functions on compact spaces without perfect subsets. Proceedings of the American Mathematical Society, 8(1), 39-39. doi:10.1090/s0002-9939-1957-0085475-7

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