Controlling disjointness with a hedgehog

Houston Journal of Mathematics

Volumn 35, Issue 2, 2009, Pages 469-484

  García, J Gutiérrez ^a   Kubiak, T ^b   De Prada Vicente, M A ^a  

^a UNIVERSITY OF THE BASQUE COUNTRY UPV EHU   (Spain)

^b ADAM MICKIEWICZ UNIVERSITY   (Poland)

Author keywords

Collectionwise normality; Absolute extensor; Collectionwise normality; Extension; Hedgehog; Lawson topology; Pairwise disjoint functions; Total z embedding

Indexed keywords

EID: 67949100425     PISSN: 03621588     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (20)

1. R. A. Alò and H. L. Shapiro, Normal Topological Spaces, Cambridge Univ. Press, Cambridge, 1974.
2. C. E. Aull, Extendability and expandability, Boll. U. M. I. (6) 5-A (1986), 129-135.
3. S. Barov and J. J. Dijkstra, On boundary avoiding selections and some extension theorems, Pacific J. Math. 203 (2002), 79-87.
4. R. L. Blair, A cardinal generalization of z-embedding, Rings of continuous functions, Lecture Notes in Pure and Applied Math. 95, Marcel Dekker Inc. 1985, 7-66.
5. R. L. Blair and M. A. Swardson, Insertion and extension of hedgehog-valued functions, Indian J. Math. 29 (1987), 229-250.
6. G. Buskes, The Hahn-Banach theorem surveyed, Dissert. Math. 327 (1993), pp. 1-49.
7. E. K. van Douwen, D. J. Lutzer and T. C. Przymusiński, Some extensions of the Tietze-Urysohn theorem, Amer. Math. Monthly 84 (1977), 435-441.
8. J. Dugundji, An extension of Tietze's theorem, Pacific J. Math. 1 (1951), 353-367.
9. R. Engelking, General Topology, Monografie Mathematyczne, Vol. 60, Polish Scientific Publishers, Warsaw, 1977; (Revised and completed ed.: Sigma Series in Pure Mathematics, Vol. 6, Heldermann Verlag, Berlin, 1989.)
10. M. Frantz, Controlling Tietze-Urysohn extensions, Pacific J. Math. 169 (1995), 53-73.
11. G. Gierz, K. H. Hofmann, K. Keimel, J. D. Lawson, M. Mislove and D. S. Scott, Continuous Lattices and Domains, Cambridge University Press, Cambridge, 2003.
12. J. Gutiérrez García, T. Kubiak and M. A. de Prada Vicente, Insertion of lattice-valued and hedgehog-valued functions, Topology Appl. 153 (2006), 1458-1475.
13. J. Gutiérrez García, T. Kubiak and M. A. de Prada Vicente, Generating and inserting continuous functions with values in bounded complete domains and hedgehog-like structures, Houston J. Math. 34 (2008), no. 1, 123-144.
14. J. Malešiǩ, D. Repovš and P. V. Semenov, On controlled extension of functions, J. Math. Anal. Appl. 285 (2003), 62-73.
15. T. Przymusiński, Collectionwise normality and absolute retracts, Fund. Math. 98 (1978), 61-73.
16. T. Przymusiński, Collectionwise normality and extensions of continuous functions, Fund. Math. 98 (1978), 75-81.
17. K. Yamazaki, A cardinal generalization of C-embedding and its applications, Topology Appl. 108 (2000), 137-156.
18. K. Yamazaki, Controlling extensions of functions and C-embedding, Topology Proc. 26 (2001), 323-341.
19. K. Yamazaki, Extending pointwise bounded equicontinuous collections of functions, Tsukuba J. Math. 29 (2005), 197-213.
20. K. Yamazaki, Controlled extension of products of continuous functions, Houston J. Math. 31 (2005), 1127-1133.