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The abstract boundary uses sets of curves with the bounded parameter property(b.p.p.) to classify the elements of the abstract boundary into regular points,singular points, points at infinity and so on. To study how the classificationchanges as this set of curves is changed it is necessary to describe therelationships between these sets of curves in a way that reflects the effect ofthe curves on the classification. The usual algebra of sets fails to do this.We remedy this situation by generalising inclusion, intersection, and union:producing an algebra of sets on the set of all b.p.p. satisfying sets of curvesthat does appropriately describe the relative effects on the classification. InPart II we use this algebra of sets to show how the classification changes asthe set of b.p.p. satisfying set of curves is changed with respect to thisgeneralization.

The dependence of the abstract boundary classification on a set of  curves I: An algebra of sets on bounded parameter property satisfying sets of  curves