Let C(X) denote the ring of all continuous real-valued functions on a completely regular space X. If X and Y are completely regular spaces such that one is dense in the other, say X is dense in Y, and every f ε C(X) has a (unique) extension f E C(Y), then C(X) and C(Y) are said to be strictly isomorphic. In a recent paper , L. J. Heider asks if it is possible to associate with the completely regular space X a dense subspace μX minimal with respect to the property that C(μX) and C(X) are strictly isomorphic.
© 1957 University of Michigan
Henriksen, Melvin. "On minimal completely regular spaces associated with a given ring of continuous functions." Michigan Mathematical Journal 4.1 (1957): 61-64. DOI: 10.1307/mmj/1028990178