Topology is the branch of mathematics that studies properties of spaces that are invariant under continuous deformations. Learn about the typical questions, examples and subfields of topology, such as general, combinatorial, algebraic and differential topology. Topology is the mathematical study of the properties that are preserved through deformations, twistings, and stretchings of objects. Tearing, however, is not allowed. A circle is topologically equivalent to an ellipse (into which it can be deformed by stretching) and a sphere is equivalent to an ellipsoid. Similarly, the set of all possible positions of the hour hand of a clock is topologically equivalent to a circle (i.e., a one-dimensional closed curve with no intersections that can be... Topology is a branch of mathematics that studies properties of space that are preserved under transformations, such as stretching, twisting, or bending, but not tearing or gluing. For example, a circle can be stretched into an ellipse without tearing or having to re-attach any lines or corners, making the two shapes topologically the same. Topology is a Greek word that means the study of place. The well-defined branch of mathematics emerged in the 20th century. Topology is used not only in different branches of mathematics like differential equations, knot theory, dynamical systems, etc but also it is used to understand physics concepts of the space-time structure of the universe and string theory. Let's discuss topology and its applications in this article.
