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edited Mar 18, 2019 at 22:45

Does the total space of a bundle satisfy the Tietze extension property when the fiber and base space do satisfy this property?

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?

gn.general-topology fibre-bundles

asked Mar 18, 2019 at 19:15

Ali Taghavi