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Dec 5, 2016 at 16:17 vote accept Phil-W
Dec 5, 2016 at 16:10 comment added Karol Szumiło Perhaps to address your question more directly I should add: it is certainly useful to know whether a given space is a retract of another. However, I'm not aware of any theory built around the notion of equivalence you are suggesting.
Dec 5, 2016 at 16:03 history answered Karol Szumiło CC BY-SA 3.0