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

Sami Lazaar, Saber Nacib


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 β◦ρ is deduced.


completely regular spaces; categories; Stone-Cech compactification

Subject classification

54D30;18B30; 54D60.

Full Text:



A. Ayech and O. Echi, The envelope of a subcategory in topology and group theory, Int. J. Math. Sci. 2005, no. 21, 3387-3404.

C. Cassidy, M. Hebert and G. M. Kelly, Reflective subcategories, localizations and factorization systems, J. Austral. Math. Soc. (Series A) 41 (1986), 286.

O. Echi and S. Lazaar, Universal spaces, Tychonoff and spectral spaces, Math. Proc. R. Ir. Acad. 109, no. 1(2009), 35-48.

P. J. Freyd and G. M. Kelly, Categories of continuous functors (I), J. Pure Appl. Algebra 2 (1972), 169-191.

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.

E. Hewitt, Rings of real-valued continuous function, I, Trans. Amer. Math. Soc. 64 (1948), 54-99.

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).

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.

R. C. Walker, The Stone-Cech Compactification, Springer-Verlag: Berlin, 1974.

Abstract Views

Metrics Loading ...

Metrics powered by PLOS ALM

Esta revista se publica bajo una licencia de Creative Commons Reconocimiento-NoComercial-SinObraDerivada 4.0 Internacional.

Universitat Politècnica de València

e-ISSN: 1989-4147