The Dugundji extension property can fail in $ω_μ$ -metrizable spaces

Volume 150 / 1996

Ian S. Stares, Jerry E. Vaughan Fundamenta Mathematicae 150 (1996), 11-16 DOI: 10.4064/fm-150-1-11-16


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.


  • Ian S. Stares
  • Jerry E. Vaughan

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