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Remarks on the rings of functions which have a finite numb er of di scontinuities

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Remarks on the rings of functions which have a finite numb er of di scontinuities

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Ahmadi Zand, MR.; Khosravi, Z. (2021). Remarks on the rings of functions which have a finite numb er of di scontinuities. Applied General Topology. 22(1):139-147. https://doi.org/10.4995/agt.2021.14332

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Título: Remarks on the rings of functions which have a finite numb er of di scontinuities
Autor: Ahmadi Zand, Mohammad Reza Khosravi, Zahra
Fecha difusión:
Resumen:
[EN] Let X be an arbitrary topological space. F(X) denotes the set of all real-valued functions on X and C(X)F denotes the set of all f ∈ F(X) such that f is discontinuous at most on a finite set. It is proved that if r ...[+]
Palabras clave: C(X)F , Z-ultrafilter , Completely separated , C(X)F -embedded , Z-filter , Over-rings of C(X) , Artinian ring
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.2021.14332
Editorial:
Universitat Politècnica de València
Versión del editor: https://doi.org/10.4995/agt.2021.14332
Agradecimientos:
Department of pure Mathematics Yazd university. We record our pleasure to the anonymous referee for his or her constructive report and many helpful suggestions on the main results of the earlier version of the manuscript ...[+]
Tipo: Artículo

References

M. R. Ahmadi Zand, An algebraic characterization of Blumberg spaces, Quaest. Math. 33, no. 2 (2010), 223-230. https://doi.org/10.2989/16073606.2010.491188

A. J. Berrick and M. E. Keating, An Introduction to Rings and Modules, Cambridge University Press, 2000. https://doi.org/10.1017/9780511608674

W. Dunham, T1/2 -spaces, Kyungpook Math. J. 17, no. 2 (1977), 161-169. [+]
M. R. Ahmadi Zand, An algebraic characterization of Blumberg spaces, Quaest. Math. 33, no. 2 (2010), 223-230. https://doi.org/10.2989/16073606.2010.491188

A. J. Berrick and M. E. Keating, An Introduction to Rings and Modules, Cambridge University Press, 2000. https://doi.org/10.1017/9780511608674

W. Dunham, T1/2 -spaces, Kyungpook Math. J. 17, no. 2 (1977), 161-169.

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

Z. Gharabaghi, M. Ghirati. and A. Taherifar, On the rings of functions which are discontinuous on a finite set, Houston J. Math. 44, no. 2 (2018), 721-739.

L. Gillman and M. Jerison, Rings of Continuous Functions, Springer-Verlag, New York-Heidelberg, 1976.

N. Levine, Generalized closed sets in topology. Rend. Circ. Mat. Palermo. 19, no. 2 (1970), 89-96. https://doi.org/10.1007/BF02843888

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