General topology
Point-set topology: the abstract study of continuity, compactness, and convergence.
Founded: 1914 — Hausdorff's Grundzüge der Mengenlehre
The claim
No credible dismissal found. This entry is a lower-confidence synthesis rather than a sourced claim; treat with appropriate caution. Constructivist/intuitionist objections (Brouwer) concerned foundations, not utility.
What happened
General equilibrium economics (1954) — Arrow & Debreu's existence proof uses Kakutani's 1941 fixed-point theorem, built on compactness (Tychonoff).
40 years — founding (1914) to Arrow–Debreu (1954)
Verdict: Never dismissed, applied anyway.
Confidence: low-medium.