What is the definition of a manifold?

What is the definition of a manifold varies by field but precise definitions exist for each. In engineering, manifold is defined as a pipe, chamber, or block with multiple inlets or outlets used to distribute fluid from one source to many destinations or collect fluid from many sources into one, acting as distribution hub with valves for control, such as intake manifold distributing air to engine cylinders. In mathematics, formal definition is that an n-dimensional manifold is a topological space that is locally homeomorphic to Euclidean space R^n, meaning every point has a neighborhood that looks like open set in R^n, and is second countable and Hausdorff, allowing calculus to be done locally even if globally curved, examples include circle as 1-manifold, sphere as 2-manifold, and our 3D space as 3-manifold. In general English, definition as adjective is many and various, having many different forms or elements. In Bible, manifold means abundant and diverse. So definition depends on context: engineering device for flow management, mathematical space that locally looks flat but globally curved, or adjective meaning numerous and varied, all sharing idea of many folds combined.