Continuum Theory is a branch of mathematics that studies properties and structures of continuous spaces. It focuses on understanding how different sets can be classified based on their size and dimensionality, particularly in relation to the concept of infinity. This theory is essential in fields like topology and analysis, where the behavior of continuous functions is examined. One of the key concepts in Continuum Theory is the continuum hypothesis, which posits that there is no set whose size is strictly between that of the integers and the real numbers. This hypothesis has significant implications in set theory and has been a central topic in mathematical discussions since the early 20th century.