Primal spaces and quasihomeomorphisms

Afef Haouati, Sami Lazaar


In [3], the author has introduced the notion of primal spaces.
The present paper is devoted to shedding some light on relations between quasihomeomorphisms and primal spaces.

Given a quasihomeomorphism q from X to Y , where X and Y are principal spaces, we are concerned specically with a main problem: what additional conditions have to be imposed on q in order to render X (resp.Y ) primal when Y (resp.X) is primal.


Quasihomeomorphism; principal space; sober space.

Subject classification

54B30; 54D10; 54F65; 54H20.

Full Text:



K. Belaid, O. Echi and S. Lazaar, $T_{(alpha , beta )$-spaces and the Wallman Compactification, Int. J. Math. Math. Sc. 68 (2004), 3717-3735.

O. Echi, Quasi-homeomorphisms, Goldspectral spaces and Jacspectral spaces, Boll. Unione Mat. Ital. Sez. B Artic. Ric. Mat. (8) (2003), 489-507.

O. Echi,The category of flows of Set and Top, Topology Appl. 159 (2012), 2357-2366.

J. F. Kennisson, The cyclic spectrum of a Boolean flow, Theory Appl. Categ. 10 (2002), 392-409.

J. F. Kennisson, Spectra of finitly generated Boolean flow, Theory Appl. Categ. 16 (2006), 434-459.

A. Grothendieck and J. Dieudonné, Eléments de Géométrie Algébrique, Die Grundlehren der mathematischen Wissenschaften, vol. 166, Springer-Verlag, New York, 1971.

A. Grothendieck and J. Dieudonné, Eléments de Géométrie Algébrique. I. Le langage des schémas, Inst. Hautes Études Sci. Publ. Math. No. 4, 1960.

H. Stone,Applications of Boolean algebra to topology, Mat. Sb. 1 (1936), 765-772.

Win K. W. Yip, Quasi-homeomorphisms and lattice-equivalences of topological spaces, J. Austral. Math. Soc. 14 (1972), 41-44.

Gierz G. Gierz, K. H. Hofmann, K. Keimel, J. D. Lawson, M. Mislove and D. S. Scott, Continuous Lattices and Domains, Cambridge Univ, Press, 2003.

Abstract Views

Metrics Loading ...

Metrics powered by PLOS ALM


Cited-By (articles included in Crossref)

This journal is a Crossref Cited-by Linking member. This list shows the references that citing the article automatically, if there are. For more information about the system please visit Crossref site

1. Primal topologies on the integers
S. García-Ferreira, A. Guale, J. Vielma
Quaestiones Mathematicae  first page: 1  year: 2019  
doi: 10.2989/16073606.2019.1695686

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

Universitat Politècnica de València

e-ISSN: 1989-4147