Study of geometric properties preserved under continuous deformations.
At the heart of topology is the idea of open and closed sets. These help us define what it means for points to be "close together" or for a set to have a "boundary."
An open set is like a neighborhood where every point has some wiggle room—all nearby points are also in the set. There's no edge or boundary included.
Closed sets, on the other hand, include their boundary points. Think of a solid ball: the surface is part of the ball, so it's closed.
These concepts allow us to talk about continuity, limits, and connectedness in a flexible, general way.
The set of all points inside a circle, not including the edge, is open.
The set of all points on and inside a circle (including the edge) is closed.
Open and closed sets help define the structure of spaces in topology.