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the term topological subspace used to redirect to the general-purpose entry subspace. I have now instead made it redirect to subspace topology and pointed to there from subspace.
(Also, at subspace I have removed a sentence which claimed that “On the nLab we often say ’space’ to mean ’topological space’.” Because on the contrary, on the $n$Lab we are dealing with general abstract mathematics and not just the small field of topology, and so we are being careful and don’t assume that “space” by default means “topological space”.)
I have added some material to topological subspace, including two lemmas, one on pushouts of (closed/open) subspaces, and a similar one on transfinite compositions of such.
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