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NOTES ON POINT-FREE REAL FUNCTIONS AND SUBLOCALES 199
Acknowledgements. Support by the Ministry of Economy and Competitive- ness of Spain (through grant MTM2012-37894-C02-02), the University of the Basque Country UPV/EHU (through grants GIU12/39 and UFI 11/52), the Centre for Mathematics of the University of Coimbra (funded by the Euro- pean program COMPETE and by the Portuguese Government through the FCT project PEst-C/MAT/UI0324/2013) and the project P202/12/G061 of the Grant Agency of the Czech Republic is gratefully acknowledged.
References
[1] R. N. Ball and J. Walters-Wayland, C- and C⇤-quotients in Pointfree Topology, Dissert. Math, Vol. 412, 2002.
[2] B. Banaschewski, Compactifications of frames, Math. Nachr. 149 (1990) 105–116.
[3] B. Banaschewski, The Real Numbers in Pointfree Topology, Textos de Matema´tica, Vol.
12, University of Coimbra, 1997.
[4] B. Banaschewski, T. Dube, C. Gilmour and J. Walters-Wayland, Oz in pointfree topol-
ogy, Quaest. Math. 32 (2010) 215–227.
[5] B. Banaschewski and C. Gilmour, Pseudocompactness and the cozero part of a frame,
Comment. Math. Univ. Carolinae 37 (1996) 577–587.
[6] B. Banaschewski, J. Guti´errez Garc´ıa and J. Picado, Extended real functions in pointfree
topology, J. Pure Appl. Algebra 216 (2012) 905–922.
[7] B. Banaschewski, S. S. Hong and A. Pultr, On the completion of nearness frames, Quaest.
Math. 21 (1998) 19–37.
[8] B. Banaschewski and A. Pultr, A constructive view of complete regularity, Kyungpook
Math. J. 43 (2003) 257–262.
[9] R. L. Blair and E. van Douwen, Nearly realcompact spaces, Topology Appl. 47 (1992)
209–221.
[10] T. Dube, On the ideal of functions with compact support in pointfree function rings,
Acta Math. Hungar. 129 (2010) 205–226.
[11] T. Dube and J. Walters-Wayland, Coz-onto frame maps and some applications, Appl.
Categ. Struct. 15 (2007) 119–133.
[12] L. Gillman and M. Jerison, Rings of Continuous Functions, Van Nostrand, 1960.
[13] J. Guti´errez Garc´ıa and T. Kubiak, General insertion and extension theorems for localic
real functions, J. Pure Appl. Algebra 215 (2011) 1198–1204.
[14] J. Guti´errez Garc´ıa, T. Kubiak and J. Picado, Pointfree forms of Dowker’s and Michael’s
insertion theorems, J. Pure Appl. Algebra 213 (2009) 98–108.
[15] J. Guti´errez Garc´ıa, T. Kubiak and J. Picado, Localic real functions: a general setting,
J. Pure Appl. Algebra 213 (2009) 1064–1074.
[16] J. Guti´errez Garc´ıa, T. Kubiak and J. Picado, Perfectness in locales, in preparation.
[17] J. Guti´errez Garc´ıa and J. Picado, On the algebraic representation of semicontinuity, J.
Pure Appl. Algebra 210 (2007) 299–306.
[18] J. Guti´errez Garc´ıa and J. Picado, Rings of real functions in pointfree topology, Topology
Appl. 158 (2011) 2264–2278.
[19] J. Guti´errez Garc´ıa and J. Picado, Insertion and extension results for point-free complete
regularity, Bull. Belg. Math. Soc. Simon Stevin 20 (2013) 675–687.
[20] R. W. Heath and E. A. Michael, A property of the Sorgenfrey line, Compositio Math. 23
(1971) 185–188.