Given a collection of multivariate inequalities (field of real numbers) I 
would like to know if the set defined is connected. Does Sage have a easy 
way through qepcad to answer such a question?

Documentation shows that there is a function connected_subset 
https://doc.sagemath.org/html/en/reference/interfaces/sage/interfaces/qepcad.html#sage.interfaces.qepcad.qepcad_formula_factory.connected_subset
But it mentions only taking a single variable
"Given a variable and a formula, returns a new formula which is true iff 
the set of values for the variable at which the original formula was true 
is connected"

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