Vol. 80, No. 2, 1979

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Isomorphisms and simultaneous extensions in C(S)

Howard Banilower

Vol. 80 (1979), No. 2, 305–311

Let h map a subspace A continuously into the completely regular space S so that A and h[A] are completely separated in S, and let Q be the quotient space of S gotten by identifying p with h(p) for all p in A. If there exists a simultaneous extension from C(A) into C(S), then there exists an isomorphism of C(S) onto itself, taking C(Q) onto C(SA), which is the identity on C(Sh[A]) (whence C(Q) is complemented in C(S)). The converse holds providing A and h[A] are normally embedded in S and h is a homeomorphism.

Mathematical Subject Classification 2000
Primary: 54C20
Secondary: 46E15, 54C25
Received: 15 December 1976
Published: 1 February 1979
Howard Banilower