What is nearby fact in maths?

In mathematics, the term "nearby fact" often refers to a concept or theorem that is closely related or similar to another known fact, making it easier to understand or prove. These nearby facts can help in building intuition or in simplifying complex proofs by drawing parallels to established results. For example, in topology, the properties of a space may be better understood by considering nearby spaces with similar characteristics. This approach can aid in exploring and discovering new mathematical relationships.