Philippines Philippines The Philippines ( ; or ' ), officially the Republic of the Philippines (), is an archipelagic country in Southeast Asia. Situated in the western Pacific Ocean, it consists of about 7,641 islands that are categorized broadly under three main geographical divisions from north to south: Luzon, Visayas, and Mindanao. The capital city of the Philippines is Manila and the most populous city is Quezon City, both part of Metro Manila. Bounded by the South China Sea on the west, the Philippine Sea on the east and the Celebes Sea on the southwest, the Philippines shares maritime borders with
Lie group–Lie algebra correspondence Lie group–Lie algebra correspondence In mathematics, Lie group–Lie algebra correspondence allows one to study Lie groups, which are geometric objects, in terms of Lie algebras, which are linear objects. In this article, a Lie group refers to a real Lie group. For the complex and "p"-adic cases, see complex Lie group and "p"-adic Lie group. In this article, manifolds (in particular Lie groups) are assumed to be second countable; in particular, they have at most countably many connected components. There are various ways one can understand the construction of the Lie algebra of a Lie group "G". One approach uses