Lebesgue quasi-uniformity on textures


  • Selma Ozcag Hacettepe University




Texture, di-uniformity, quasi-uniformity, Lebesgue quasi-uniformity.


This is a continuation of the work where the notions of Lebesgue uniformity and Lebesgue quasi uniformity in a texture space were introduced. It is  well known that the quasi uniform space with a compact topology has the Lebesgue property. This result is extended to direlational quasi uniformities and dual dicovering quasi uniformities. Additionally we discuss the completeness of lebesgue di-uniformities and dual dicovering lebesgue di-uniformities.


Download data is not yet available.

Author Biography

Selma Ozcag, Hacettepe University

Mathematics Department


L. M. Brown, Dual covering theory, confluence structures and the lattice of bicontinuous functions, Ph.D. Thesis, Glasgow University, 1981.

L. M. Brown and M. Diker, Paracompactness and full normality in ditopological texture spaces, Journal of Mathematical Analysis and Applications, 227 (1998) 144-165. http://dx.doi.org/10.1006/jmaa.1998.6090

L. M. Brown and R. Ertürk, Fuzzy sets as texture spaces I. representations theorems, Fuzzy Sets andSystems, 110, no. 2 (2000) 227-236.


L. M. Brown, R. Ertürk, and S. Dost, Ditopological texture spaces and fuzzy topology, I. Basic Concepts, Fuzzy Sets and Systems, 147, no. 2 (2004), 171-199. http://dx.doi.org/10.1016/j.fss.2004.02.009

L. M. Brown and M. M. Gohar, Compactness in Ditopological Texture Spaces}, Hacettepe journal of Mathematics and Statistics 38, no. 1 (2009), 21--43.

P. Fletcher and W. F. Lindgren, Quasi-uniform spaces, Marcel Dekker, (New York and Basel, 1982).

T. E. Gantner and R. G. Steinlage, Characterizations of quasi uniformities, Jounal of London Mathematical Sociey 11, no. 5 (1972), 48-52.


H.P.A. Kunzi, An introduction to quasi-uniform spaces, In: Beyond Topology, Contemporary Mathematics, (F. Mynard And E. Pearl eds), American mathematical society, Vol.468 (2009) 239--304.

B. Hutton, Uniformities on fuzzy topological spaces, Journal of Mathematical Analysis and Applications 58 (1977), 559-571. http://dx.doi.org/10.1016/0022-247X(77)90192-5

J. Marin and S. Romaguera, On quasi uniformly continuous functions and Lebesgue spaces}, Publicationes Mathematicae Debrecen 48 (1996), 347-355.

S. Özcag and L. M. Brown, Di-uniform texture spaces}, Applied General Topology 4, no. 1 (2003), 157-192. http://dx.doi.org/10.4995/agt.2003.2017

S. Özcag, F. Yildiz and L. M. Brown, Convergence of regular difilters and the completeness of di-uniformities, Hacettepe Journal of mathematics and statistics 34, (2005) 53-68.

S. Özcag and L. M. Brown, A textural view of the distinction between uniformities and quasi-uniformities, Topology and its Applications 153 (2006), 3294-3307. http://dx.doi.org/10.1016/j.topol.2005.03.018

S. Özcag, Lebesgue and co-lebesgue di-uniform texture spaces, Topology and its Applications 156 (2009), 3021-3028. http://dx.doi.org/10.1016/j.topol.2009.01.021

S. Özcag, The concept of quasi uniformity in texture space and its representations, Questiones Mathematicae 33 (2010), 457-476. http://dx.doi.org/10.2989/16073606.2010.541621

S. Özcag, L. M. Brown and B. Krsteska, Di-uniformities and Hutton uniformities, Fuzzy sets and Systems 195 (2012), 58-74. http://dx.doi.org/10.1016/j.fss.2011.12.004




How to Cite

S. Ozcag, “Lebesgue quasi-uniformity on textures”, Appl. Gen. Topol., vol. 16, no. 2, pp. 167–181, Oct. 2015.



Regular Articles