Unless he takes a flight, then he lives on a manifold.Math_QED said:
If I say that: There is a ball that is bouncing.HallsofIvy said:
Living room?pairofstrings said:
A rose by any other name would smell as sweet.pairofstrings said:
The ball exists in a space of three spatial dimensions and one temporal (time measurement) dimension. As the ball moves up or down, its position in the spatial dimensions changes, and the time changes.pairofstrings said:
The "Mathematical Name of this Space" refers to a mathematical concept known as a topological space. It is a set of points with a defined structure that allows for the study of continuity and convergence.
A topological space is defined by a set of points and a collection of subsets of those points, known as open sets. These open sets satisfy certain axioms, such as being closed under finite intersections and arbitrary unions, and allow for the study of continuity and convergence.
Studying topological spaces allows for a deeper understanding of the properties of continuous functions and their behavior. It also has applications in various fields such as physics, computer science, and economics.
A metric space is a type of topological space that has an additional structure known as a metric, which measures the distance between points. In a topological space, the concept of distance is not necessary, and the focus is on the overall structure of the space.
One example of a topological space is the real line, which consists of all real numbers and is defined by the standard topology. Other examples include the Euclidean space, the unit circle, and the Cantor set.