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Monotone insertions of continuous functions - University of ...

Monotone insertions of continuous functions - University of ...

14 CHRIS GOOD AND IAN

14 CHRIS GOOD AND IAN STARES References [1] R. L. Blair and M. A. Swardson, Insertion and extension of hedgehog-valued functions, Indian J. Math. 29 (1987), 229-250. [2] C. J. R. Borges, A study of monotonically normal spaces, Proc. Amer. Math. Soc. 38 (1973), 211-214. [3] J. Dieudonné, Une généralisation des espaces compacts, J. Math. Pures et Appl. 23 (1944), 65-76. [4] E. K. van Douwen, Simultaneous extension of continuous functions, in J. van Mill, ed., Eric K. van Douwen, Collected Papers, Volume 1, North-Holland, Amsterdam, 1994. [5] C. H. Dowker, On countably paracompact spaces, Canad. J. Math. 3 (1951), 219-224. [6] R. Engelking, General topology, Sigma Series in Pure Mathematics, Vol. 6, Heldermann Verlag, Berlin, 1989. [7] C. Good, R. Knight and I. Stares, Monotone countable paracompactness, to appear in Top Appl. [8] G. Gruenhage, Generalized metric spaces in Handbook of set-theoretic topology, K. Kunen and J. E. Vaughan, eds., North-Holland, Amsterdam, 1984. [9] H. Hahn, Über halbstetige und unstetige Funktionen, Sitzungsberichte Akad. Wiss. Wien Abt. IIa 126 (1917), 91-110. [10] R. W. Heath, D. J. Lutzer, and P. L. Zenor, Monotonically normal spaces, Trans. Amer. Math. Soc. 178 (1973), 481-493. [11] M. Katětov, On real-valued function in topological spaces, Fund. Math. 38 (1951) 85-91 [12] T. Kubiak, Monotone insertion of continuous functions, Question Answers Gen. Topology 11 (1993), 51-59. [13] E. Lane, Insertion of continuous functions, Topology Proc. 4 (1979), 463-478. [14] M. Mandelkern, A short proof of the Tietze-Urysohn extension theorem, Arch. Math. (Basel) 60 (1993), 364-366. [15] E. Michael, Continuous selections I, Annals of Math. 63 (1956), 361-382. [16] P. Nyikos and C. Pan, Monotone insertion properties of stratifiable spaces, to appear. [17] C. Pan, Monotonically CP spaces, to appear. [18] I. S. Stares, Monotone normality and extension of functions, Comment. Math. Univ. Carolinae 36 (1995), 563-578. [19] H. Tong, Some characterizations of normal and perfectly normal spaces, Duke Math. J. 19 (1952), 289-292. School of Mathematics and Statistics, University of Birmingham, Birmingham, B15 2TT, United Kingdom E-mail address: c.good@bham.ac.uk Mathematical Institute, 24-29 St Giles’, Oxford OX1 3LB, United Kingdom E-mail address: isstares@maths.ox.ac.uk

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