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Jun 26 at 17:02 vote accept Ondrej Draganov
Jun 22 at 8:20 comment added Tyrone If the pairs $(X,A), (Y,B)$ have the homotopy extension property, then this holds. It also holds when the two pairs have the weak homotopy extension property. I'm not sure much more can be said without strengthening the assumptions somewhat.
Jun 22 at 8:20 answer added HenrikRüping timeline score: 4
Jun 21 at 13:47 comment added HenrikRüping A 'bad' example is the case of $(S^1,(1,0))$ and $(S^1,S^1\setminus (-1,0))$ and the map is the identity.
Jun 21 at 11:52 history asked Ondrej Draganov CC BY-SA 4.0