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Tietze Extension T Heorem
Definition: Let X be a normal space; let A be a closed subspace of X. (a) Any Continuous map of A into the closed interval [a, b] of R may be extended to a continuous map of all of X into [a, b]. (b) Any continuous map of A into R may be extended to a continuous map of all of X into R.
Source: Topology (second edition) by James R. Munkres