Metrizable spaces

A metrizable space is a type of mathematical space where the concept of "distance" between points is well-defined through a metric. This means you can measure how far apart two points are using a function that satisfies certain properties (non-negativity, symmetry, triangle inequality, and that zero distance only occurs when points are the same). Metrizable spaces help connect abstract topological concepts with intuitive notions of distance, allowing a more tangible understanding of continuity, convergence, and shape within the space. Many familiar spaces, like Euclidean space, are examples of metrizable spaces.