What is the definition of a manifold in differential geometry?

a$)$ It is a topological space that locally resembles Euclidean space near each point.

b$)$ It is a set of points that are equidistant from a given point, forming a circle in two dimensions.

c$)$ It is a geometric object that can be smoothly mapped onto a Euclidean space.

d$)$ It is a set of points in space that satisfy a system of linear equations.