Eilenberg-Steenrod axioms

The Eilenberg-Steenrod axioms are a set of rules that define what properties a mathematical way of measuring spaces (called homology or cohomology) should have to be consistent and meaningful. They ensure that these measurements are unaffected by small changes, behave predictably with spaces built from simpler parts, and behave well when combining or splitting spaces. These axioms help mathematicians develop consistent tools to analyze the shape, structure, and features of complex spaces in a rigorous way.