The Dugundji extension property can fail in ωµ -metrizable spaces

• Autorzy: Ian S. Stares , Jerry E. Vaughan
• Języki publikacji: EN

Abstrakty

EN

We show that there exist $ω_μ$-metrizable spaces which do not have the Dugundji extension property ($2^{ω_1}$ with the countable box topology is such a space). This answers a question posed by the second author in 1972, and shows that certain results of van Douwen and Borges are false.

Słowa kluczowe

EN

Dugundji extension theorem; $ω_μ$-metrizable spaces; box topology; Baire category; Michael line

Kategorie tematyczne

• 54E52: Baire category, Baire spaces
• 54E15: Uniform structures and generalizations
• 54C20: Extension of maps
• 54H11: Topological groups

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 1996
• Tom: 150
• Numer: 1
• Strony: 11-16

Daty

wydano

1996

otrzymano

1995-05-19

poprawiono

1995-11-07

Twórcy

autor

Ian S. Stares

• Department of Mathematical, Sciences University of North Carolina at Greensboro Greensboro, North Carolina 27410, U.S.A.

autor

Jerry E. Vaughan

• Department of Mathematical, Sciences University of North Carolina at Greensboro Greensboro, North Carolina 27410, U.S.A.

Bibliografia

• [1] C. J. R. Borges, On stratifiable spaces, Pacific J. Math. 17 (1966), 1-16.
• [2] C. J. R. Borges, Absolute extensor spaces: a correction and an answer, Pacific J. Math. 50 (1974), 29-30.
• [3] K. Borsuk, Über Isomorphie der Funktionalräume, Bull. Internat. Acad. Polon. Ser. A 1933 (1//3), 1-10.
• [4] J. Ceder, Some generalizations of metric spaces, Pacific J. Math. 11 (1961), 105-125.
• [5] W. W. Comfort and S. Negrepontis, The Theory of Ultrafilters, Springer, New York, 1974.
• [6] E. K. van Douwen, Simultaneous extension of continuous functions, in: E. K. van Douwen, Collected Papers, Vol. 1, J. van Mill (ed.), North-Holland, Amsterdam, 1994.
• [7] J. Dugundji, An extension of Tietze's theorem, Pacific J. Math. 1 (1951), 353-367.
• [8] R. Engelking, On closed images of the space of irrationals, Proc. Amer. Math. Soc. 21 (1969), 583-586.
• [9] R. Engelking, General Topology, Sigma Ser. Pure Math. 6, Heldermann, Berlin, 1989.
• [10] R. W. Heath and D. J. Lutzer, Dugundji extension theorems for linearly ordered spaces, Pacific J. Math. 55 (1974), 419-425.
• [11] P. J. Nyikos and H. C. Reichel, Topological characterizations of $ω_μ$-metrizable spaces, Topology Appl. 44 (1992), 293-308.
• [12] I. S. Stares, Concerning the Dugundji extension property, Topology Appl. 63 (1995), 165-172.
• [13] J. E. Vaughan, Linearly stratifiable spaces, Pacific J. Math. 43 (1972), 253-265.
• [14] S. W. Williams, Box products, in: Handbook of Set-Theoretic Topology, North-Holland, 1984, 169-200.
• ---