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Ali Taghavi
Ali Taghavi
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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 $Y$"$\mathbb{R}$" can be replaced by "$\mathbb{R}$"$Y$.

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?

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

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?

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?

Source Link
Ali Taghavi
Ali Taghavi
  • 356
  • 8
  • 31
  • 123

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 $Y$ can be replaced by "$\mathbb{R}$".

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?