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A theory which satisfies all the Eilenberg-Steenrod Axioms with the possible exception of the Long Exact Sequence of a Pair Axiom, as well as a certain additional continuity Condition.
References
Hazewinkel, M. (Managing Ed.). Encyclopaedia of Mathematics: An Updated and Annotated Translation
of the Soviet ``Mathematical Encyclopaedia.'' Dordrecht, Netherlands: Reidel, p. 68, 1988.