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Keywords:
insertion of continuous functions; normality; countable paracompactness; perfect
insertion of continuous functions; normality; countable paracompactness; perfect
Summary:
We provide new proofs for the classical insertion theorems of Dowker and Michael. The proofs are geometric in nature and highlight the connection with the preservation of normality in products. Both proofs follow directly from the Kat\v{e}tov-Tong insertion theorem and we also discuss a proof of this.
References:
[1] Bonan E.: Sur un lemme adapté au théorème de Tietze-Urysohn. C.R. Acad. Paris Sér. A 270 (1970), 1226-1228. MR 0257961 | Zbl 0193.51103
[2] Dieudonné J.: Une généralisation des espaces compacts. J. Math. Pures Appl. 23 (1944), 65-76. MR 0013297
[3] Dowker C.H.: On countably paracompact spaces. Canad. J. Math. 3 (1951), 219-224. MR 0043446 | Zbl 0042.41007
[4] Engelking R.: General Topology. Helderman Verlag, Berlin, 1989. MR 1039321 | Zbl 0684.54001
[5] Hahn H.: Über halbstetige und unstetige Funktionen. Sitzungsberichte Akad. Wiss. Wien Abt. IIa 126 (1917), 91-110.
[6] Katětov M.: Complete normality of Cartesian products. Fund. Math. 36 (1948), 271-274. MR 0027501
[7] Katětov M.: On real-valued functions in topological spaces. Fund. Math. 38 (1951), 85-91. MR 0050264
[8] Katětov M.: Correction to ``On real-valued functions in topological spaces''. Fund. Math. 40 (1953), 203-205. MR 0060211 | Zbl 0053.12304
[9] Lane E.P.: Insertion of a continuous function and $X\times I$. Topology Proc. 6 (1981), 329-334. MR 0672464
[10] Lane E.P.: A conjecture concerning $X\times I$. Questions Answers Gen. Topology 8 (1990), 387-403. MR 1065287 | Zbl 0721.54012
[11] Mandelkern M.: A short proof of the Tietze-Urysohn extension theorem. Arch. Math. (Basel) 60 (1993), 364-366. MR 1206320 | Zbl 0778.54005
[12] Michael E.: A note on paracompact spaces. Proc. Amer. Math. Soc. 4 (1953), 831-838. MR 0056905 | Zbl 0052.18701
[13] Michael E.: Continuous selections I. Annals of Math. 63 (1956), 361-382. MR 0077107 | Zbl 0071.15902
[14] Rudin M.E.: Dowker spaces. in: Handbook of Set-Theoretic Topology, North Holland, Amsterdam, 1984, pp.761-780. MR 0776636 | Zbl 0566.54009
[15] Scott B.M.: A ``more topological'' proof of the Tietze-Urysohn theorem. Amer. Math. Monthly 85 (1988), 117-123. MR 0474185
[16] Tong H.: Some characterizations of normal and perfectly normal spaces. Duke Math. J. 19 (1952), 289-292. MR 0050265 | Zbl 0046.16203
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