2105.02171
ITERATIVE SQUARE ROOTS OF FUNCTIONS
B.V. RAJARAMA BHAT, CHAITANYA GOPALAKRISHNA
correcthigh confidence
- Category
- math.DS
- Journal tier
- Specialist/Solid
- Processed
- Sep 28, 2025, 12:56 AM
- arXiv Links
- Abstract ↗PDF ↗
Audit review
The paper rigorously proves that W_m(2) contains no open ball in C(I^m) (Theorem 3.8), hence its interior is empty . The model’s argument hinges on a mis-stated “non-square criterion” that uses only first preimages, whereas the paper’s actual obstruction (Theorem 2.4) requires a non-fixed point x0 with infinite second preimage and finiteness of all other fibers . The model’s construction does not ensure f(a) ≠ a and only controls fibers over preimages of a, while the paper’s proof enforces the needed conditions via a local barycentric modification and explicitly verifies Case (ii) of Theorem 2.4 .
Referee report (LaTeX)
\textbf{Recommendation:} minor revisions
\textbf{Journal Tier:} specialist/solid
\textbf{Justification:}
The manuscript presents a robust, general method (via Theorem 2.4) to obstruct iterative square roots and uses it to show that maps without square roots are dense on cubes (uniform topology) and on R\^m (compact-open topology). The main result that W\_m(2) has empty interior follows cleanly from a careful piecewise affine construction. The work is precise and self-contained, with only minor editorial issues that do not affect correctness.