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We say that a Topological space $Y$ satisfies the Tietze extension propery, TE property, if in the formulation of Tietze extension theorem "$\mathbb{R}$" can be replaced by $Y$.

Obvioysly the product of two TE spaces is again a TE space. But what about a twist product? More precisely assume that the fiber and base space of a fiber bundle satisfy TE property. Is the total space necessaryly a TE space?

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  • $\begingroup$ Shouldn't it be "$\mathbb{R}$ replaced by $Y$"? The usual name is an absolute extensor (for normal spaces), I believe. $\endgroup$
    – Henno Brandsma
    Commented Mar 18, 2019 at 21:12
  • $\begingroup$ @HennoBrandsma yes thank you. I revised it. $\endgroup$
    – Ali Taghavi
    Commented Mar 18, 2019 at 22:45
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    $\begingroup$ If $Y$ is a Polish space, then the answer affirmative (which can be proved applying the theory of absolute retracts). $\endgroup$
    – Taras Banakh
    Commented Mar 21, 2019 at 18:05

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