A topological space is a fundamental concept in mathematics, particularly in the field of topology. It consists of a set of points, along with a collection of open sets that satisfy certain properties. These open sets help define how the points relate to each other in terms of closeness and continuity, without necessarily relying on distance. In a topological space, we can explore various properties like connectedness and compactness. These properties allow mathematicians to study shapes and spaces in a more abstract way, leading to insights in areas such as analysis, geometry, and even data science.