  We discuss the possible role of the Tietze extension theorem in providing a
rigorous topological base to the expanding space-time in cosmology. A simple
toy model has been introduced to show the analogy between the topological
extension from a circle $S$ to the whole space $M$ and the cosmic expansion
from a non-zero volume to the whole space-time in non-singular cosmological
models. A topological analogy to the cosmic scale factor function has been
suggested, the paper refers to the possible applications of the topological
extension in mathematical physics.
