nLab binormal topological space

Let I=[0.1]I = [0.1] be the closed unit interval with the standard topology. A topological space is binormal if X×IX\times I is a normal topological space (satisfies separation axioms T 4T_4 and T 1T_1).

Exercise I.B2 in Spanier: If XX is a binormal space, YY a normal space and f:XYf:X\to Y continuous, the mapping cylinder of ff is a normal space.

Borsuk’s homotopy extension theorem. (Exercise I.D2 in Spanier) Let AA be a closed subspace of a binormal space XX. Then (X,A)(X,A) has the homotopy extension property with respect to any absolute neighborhood retract YY.

  • Edwin H. Spanier, Algebraic topology, Springer 1966
category: topology

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