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I found a reference for the definition of a topological pair. I think this is the correct term and that the page on ""pair of spaces"" should be merged into this one. The refence it gives is to Hatcher, but he only uses the phrase ""pair of spaces"" informally. He does not say anywhere that this is the definition of a pair of spaces. Hatcher does talk about CW pairs, and this might be worth added note. I do not know how to merge pages, so I'll leave that for others. -MCS, Feb 20, 2014."