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What is known about these "explicitly represented" spaces?
Apologies if this is too low-level. A related question that I asked on the Math Stack Exchange got no answers after a year, so I thought it might be better to ask this one here.
The standard approach ...
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Given a sequence of reals, we can find a dense sequence avoiding it, but can we find one continuously?
Let $S$ be the set of injective sequences in $\mathbb{R}$:
$$S = \{s: \mathbb{N} \rightarrow \mathbb{R}: s(m) \neq s(n) \text{ if }m \neq n\}.$$
Consider $S$ with the topology of pointwise convergence,...
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