What term is most appropriate when describing the infinite space of possibilities created through inductive reasoning?

It might not be possible to come up with a term that is accessible by the general population simply because what the term is supposed to describe is unknown to the general population.

Either someone reading your text is someone from the field in question, a professional, or they are a layperson. If they are a professional they'd prefer a term that makes sense given your theory and the field in question, so it doesn't matter if it's technical or ambiguous in other contexts. If the person reading your text is a layperson they would not benefit from one term being more accessible as long as your whole theory is not as accessible.

Thus, I'd suggest that you come up with a term that makes sense within your theory and field. What you seem to speak of is possibilities given premises. These can be construed through concepts such as solution spaces, probability spaces or sets of possible worlds. It's important that the term you choose is consistent with how you speak of possibility in any other place in your theory, e.g. if you speak of possibilities as sets of possible worlds you should only speak of possibility that way to avoid confusion. Even if you use technical terms they can be more or less self-explanatory, so choose them carefully. For instance if you speak of sets of possible world you could say that the set of possible worlds expressed by a deduction is a subset of the set of possible worlds expressed by the premises, but the set of possible worlds expressed by the conclusion of an induction can be a superset of the set of possible worlds expressed by the premises. By comparing cardinality of sets of possible world it might also be possible to effectively communicate their size and infinity (I'm just guessing here, dunno what you want to say).

If you still want a term that a layperson understand you might want to speak of possibilities so that keep close to common talk of possibility, i.e. how possibility is conceived of and discussed in everyday situations. For example you could say that given some conditions there is greater or wider possibility than given some other conditions.

Finally, in both cases examples are powerful tools to illustrate terms you want to define. A good example can make a theory easier to understand and remember.

Both your suggestions solution space and induction space are appropriate for different reasons.

Solution space works because it is very specific and your concept seems to be about solutions to a problem that come from a given set.

Induction space does seem to be use in widely different ways in your google link, but that's because it is very non-specific and so can be used locally and disambiguated with the context (and your own explicit definition).