While Begle's contributions to the field of mathematical research are limited, among them is the first proof of the Vietoris theorem, which caused it to become commonly known as the Vietoris–Begle mapping theorem.
Liouville's theorem | Christian Vietoris | Chinese remainder theorem | Shannon–Hartley theorem | Quillen–Suslin theorem | Nyquist–Shannon sampling theorem | Hahn–Banach theorem | Fermat's Last Theorem | Buckingham π theorem | Thue–Siegel–Roth theorem | Texture mapping | Szemerédi's theorem | Semantic mapping | Schottky's theorem | Riemann-Roch theorem | Pythagorean theorem | Nash embedding theorem | Müntz–Szász theorem | Malgrange–Ehrenpreis theorem | Kleene fixed-point theorem | Kakutani fixed-point theorem | Gauss–Bonnet theorem | Doob's martingale convergence theorem | Dirichlet's theorem on arithmetic progressions | Denjoy theorem | Birch's theorem | Wilkie's theorem | Wick's theorem | Whitney extension theorem | Weierstrass theorem |
Luck was on Maldonado's side though, as he had the lapped car of Vladimir Arabadzhiev between he and Vietoris, and an awful restart from the Bulgarian allowed Maldonado to pull out more than 3.0s on the first lap back under greens.
As with unit disk graphs, the Vietoris–Rips complex has been applied in computer science to model the topology of ad hoc wireless communication networks.