theorems of general topology

Theorems in general topology are proven statements that describe properties of spaces that form the foundation of shape, size, and connectivity. They explore how spaces can be separated, covered, or connected, such as the famous Urysohn’s lemma showing how points and sets can be distinguished by functions, or the Tychonoff theorem stating that any product of compact spaces remains compact. These results help us understand complex structures by revealing consistent patterns and behaviors, enabling mathematicians to analyze spaces abstractly and apply these insights across disciplines like physics, computer science, and engineering.