G-Man (Half-Life) refers to simply as his "employers". His mysterious nature has made him an icon of the "Half-Life" series, with his identity and motives remaining almost completely unexplained. The G-Man's name comes from "G-Man", an American colloquialism meaning "Government Man". However, within the "Half-Life" games, he is identified by this name only in the program code and the multiplayer profile menu as a default name option, not within the story itself; his name is derived from his "Half-Life" model and entity name and has since been reused in subsequent games of the series. His name has been confirmed and he has
(G,X)-manifold (G,X)-manifold If X is a manifold with an action of a topological group G by analytical diffeomorphisms, the notion of a (G, X)-structure on a topological space is a way to formalise it being locally isomorphic to X with its G-invariant structure; spaces with a (G, X)-structures are always manifolds and are called (G, X)-manifolds. This notion is often used with G being a Lie group and X a homogeneous space for G. Foundational examples are hyperbolic manifolds and affine manifolds. Let formula_1 be a connected differential manifold and formula_2 be a subgroup of the group of diffeomorphisms of formula_1