We will form a proof of the Arzela-Ascoli Theorem through use of the Heine-Borel theorem. We will also be considering some notions of compactness on metric spaces. The Arzela-Ascoli Theorem then allows us to show compactness, letting us state and prove Peano's existence theorem, pertaining to the existence of the solutions of a type of ODE. Then we will state the Kolmogorov-Riesz compactness theorem, allowing us to show compactness in $L^p$ spaces, building from the Arzela-Ascoli Theorem.
Behavioural observations on the critically endangered Long-billed vultures (Gyps indicus) at Adarwadi nesting cliff in Tamhini Ghat, Maharashtra, India.
Nests and perches identified and statistical data collected for the same.
Dr Anand Padhye Kshitija Kulkarni Devna Arora Soham Dixit Neelesh Dahanukar