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$\newcommand\Top{\mathrm{Top}}\newcommand\CW{\mathrm{CW}}\newcommand\Deltagenerated{\text{$\Delta$-generated}}\newcommand\Spaces{\mathrm{Spaces}}\newcommand\DeltaSpaces{\text{$\Delta$-Spaces}}$I am ...

In the Lifting theorem for finite spaces (Thm. 3.5, Eric Wofsey, quoted below), can one relax the condition "$A$ is a closed subset of a perfectly normal $X$" to "$A\to X$ has the right ...