aka topological invariant

Properties of Topological spaces which are invariant under Homeomorphisms

• Cardinal functions (Cardinality)
• Separation axiom
  • T1
  • Hausdorff
• Connectedness
• Countability axiom
  • First countable
  • Second countable
• Compactness
• Metrizability
• Fundamental group (invariant for path-connected)
• Homotopy group – Cohomotopy group
• Homology and cohomology..
• Alexandrov space.

Invariant is used more for algebraic properties, while property more for purely topological ones.

See Homeomorphism

https://en.wikipedia.org/wiki/Topological_property