# The Dugundji extension property can fail in ωµ -metrizable spaces

Fundamenta Mathematicae (1996)

- Volume: 150, Issue: 1, page 11-16
- ISSN: 0016-2736

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topStares, Ian, and Vaughan, Jerry. "The Dugundji extension property can fail in ωµ -metrizable spaces." Fundamenta Mathematicae 150.1 (1996): 11-16. <http://eudml.org/doc/212158>.

@article{Stares1996,

abstract = {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.},

author = {Stares, Ian, Vaughan, Jerry},

journal = {Fundamenta Mathematicae},

keywords = {Dugundji extension theorem; $ω_μ$-metrizable spaces; box topology; Baire category; Michael line; -metrizable spaces; unbounded monotone extension; linearly stratifiable spaces},

language = {eng},

number = {1},

pages = {11-16},

title = {The Dugundji extension property can fail in ωµ -metrizable spaces},

url = {http://eudml.org/doc/212158},

volume = {150},

year = {1996},

}

TY - JOUR

AU - Stares, Ian

AU - Vaughan, Jerry

TI - The Dugundji extension property can fail in ωµ -metrizable spaces

JO - Fundamenta Mathematicae

PY - 1996

VL - 150

IS - 1

SP - 11

EP - 16

AB - 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.

LA - eng

KW - Dugundji extension theorem; $ω_μ$-metrizable spaces; box topology; Baire category; Michael line; -metrizable spaces; unbounded monotone extension; linearly stratifiable spaces

UR - http://eudml.org/doc/212158

ER -

## References

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- [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. Zbl0302.54017
- [11] P. J. Nyikos and H. C. Reichel, Topological characterizations of ${\omega}_{\mu}$-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. Zbl0226.54027
- [14] S. W. Williams, Box products, in: Handbook of Set-Theoretic Topology, North-Holland, 1984, 169-200.
- </REFERENCES>

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