Topological Property

A topological property is a feature of a topological space that stays unchanged under a homeomorphism.

In simple terms, if two topological spaces are homeomorphic (meaning there's a continuous, one-to-one correspondence between them, with a continuous inverse), they share the same topological properties.

For example, being a Hausdorff space is a topological property. If one space has this property and there’s a homeomorphism connecting it to another space, then the other space must also be Hausdorff.

Other topological properties include connectedness, compactness, and separability.

In short, a property is considered topological if it is preserved under a homeomorphism.

This idea is key in topology because it helps us compare different spaces and figure out if they are essentially "equivalent" from a topological standpoint.

And so on.