The hull orthogonal of the unit inteval [0,1]

Authors

  • Sami Lazaar University Tunis-El Manar
  • Saber Nacib University of Gafsa

DOI:

https://doi.org/10.4995/agt.2018.8981

Keywords:

completely regular spaces, categories, Stone-Cech compactification

Abstract

In this paper, the full subcategory Hcomp of Top whose objects are Hausdorff compact spaces is identified as the orthogonal hull of the unit interval I = [0,1]. The family of continuous maps rendered invertible by the reflector βâ—¦ρ is deduced.

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Author Biographies

Sami Lazaar, University Tunis-El Manar

Faculty of Sciences

Saber Nacib, University of Gafsa

Faculty of Sciences

References

A. Ayech and O. Echi, The envelope of a subcategory in topology and group theory, Int. J. Math. Sci. 2005, no. 21, 3387-3404. https://doi.org/10.1155/IJMMS.2005.3387

C. Cassidy, M. Hebert and G. M. Kelly, Reflective subcategories, localizations and factorization systems, J. Austral. Math. Soc. (Series A) 41 (1986), 286. https://doi.org/10.1017/S1446788700033693

O. Echi and S. Lazaar, Universal spaces, Tychonoff and spectral spaces, Math. Proc. R. Ir. Acad. 109, no. 1(2009), 35-48. https://doi.org/10.3318/PRIA.2008.109.1.35

P. J. Freyd and G. M. Kelly, Categories of continuous functors (I), J. Pure Appl. Algebra 2 (1972), 169-191. https://doi.org/10.1016/0022-4049(72)90001-1

L. Gillman and M. Jerison, Rings of continuous functions, Springer-Verlag (1976).

A. Haouati and S. Lazaar, Real-compact spaces and the real line orthogonal, Topology Appl. 209 (2016), 30-32. https://doi.org/10.1016/j.topol.2016.05.024

E. Hewitt, Rings of real-valued continuous function, I, Trans. Amer. Math. Soc. 64 (1948), 54-99. https://doi.org/10.1090/S0002-9947-1948-0026239-9

D. Holgate, Linking the closure and orthogonality properties of perfect morphisms in a category, Comment. Math. Univ. Carolin. 39, no. 3 (1998), 587-607.

S. MacLane, Categories for the Working Mathematician, Graduate Texts in Math. Vol. 5, Springer-Verlag, New York, (1971). https://doi.org/10.1007/978-1-4612-9839-7

M. H. Stone, On the compactification of topological spaces, Ann. Soc. Polon. Math. 21 (1948), 153-160.

W. Tholen, Reflective subcategories, Topology Appl. 27 (1987), 201-212. https://doi.org/10.1016/0166-8641(87)90105-2

R. C. Walker, The Stone-Cech Compactification, Springer-Verlag: Berlin, 1974. https://doi.org/10.1007/978-3-642-61935-9

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Published

2018-10-04

How to Cite

[1]
S. Lazaar and S. Nacib, “The hull orthogonal of the unit inteval [0,1]”, Appl. Gen. Topol., vol. 19, no. 2, pp. 245–252, Oct. 2018.

Issue

Section

Regular Articles