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ISSN 1088-6826(e) ISSN 0002-9939(p)

Local homeomorphisms via ultrafilter convergence

Author(s): Maria Manuel Clementino; Dirk Hofmann; George Janelidze
Journal: Proc. Amer. Math. Soc. 133 (2005), 917-922.
MSC (2000): Primary 54C10, 54A20, 54B30, 18A20, 18B30
Posted: August 24, 2004
MathSciNet review: 2113944
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Abstract | References | Similar articles | Additional information

Abstract: Using the ultrafilter-convergence description of topological spaces, we generalize Janelidze-Sobral characterization of local homeomorphisms between finite topological spaces, showing that local homeomorphisms are the pullback-stable discrete fibrations.

References:

1.: A. Burroni, -catégories, Cahiers Topologie Géom. Différentielle 12 (1971), 215-321. MR 46:7350
2.: M. M. Clementino, On finite triquotient maps, J. Pure Appl. Algebra 168 (2002), 387-389.
3.: M. M. Clementino and D. Hofmann, Triquotient maps via ultrafilter convergence, Proc. Amer. Math. Soc. 130 (2002), 3423-3431. MR 2003e:54012
4.: M. M. Clementino, D. Hofmann and W. Tholen, The convergence approach to exponentiable maps, Port. Math. 60 (2003), 139-160.
5.: M. M. Clementino and W. Tholen, Metric, topology and multicategory - a common approach, J. Pure Appl. Algebra 179 (2003), 13-47.
6.: G. Janelidze and M. Sobral, Finite preorders and topological descent I, J. Pure Appl. Algebra 175 (2002), 187-205. MR 2004c:18002
7.: J. Reiterman and W. Tholen, Effective descent maps of topological spaces, Top. Appl. 57 (1994), 53-69. MR 95f:18008

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Additional Information:

Maria Manuel Clementino
Affiliation: Departamento de Matemática, Universidade de Coimbra, 3001-454 Coimbra, Portugal
Email: mmc@mat.uc.pt

Dirk Hofmann
Affiliation: Departamento de Matemática, Universidade de Aveiro, 3810-193 Aveiro, Portugal
Email: dirk@mat.ua.pt

George Janelidze
Affiliation: A. Razmadze Mathematical Institute, Georgian Academy of Sciences, Tbilisi, Georgia
Email: gjanel@rmi.acnet.ge

DOI: 10.1090/S0002-9939-04-07569-0
PII: S 0002-9939(04)07569-0
Keywords: Local homeomorphism, discrete fibration, ultrafilter
Received by editor(s): May 30, 2003
Received by editor(s) in revised form: November 8, 2003
Posted: August 24, 2004
Additional Notes: The authors acknowledge partial financial assistance by Centro de Matemática da Universidade de Coimbra/FCT and Unidade de Investigação e Desenvolvimento Matemática e Aplicações da Universidade de Aveiro/FCT
Communicated by: Alan Dow
Copyright of article: Copyright 2004, American Mathematical Society

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