Abstract
Introduction. The word shall mean the graph of a real function, and the X-projection of a graph F is the set of all abscissas of points of F. c denotes the cardinality of the continuum. If H is a collection of sets, H* denotes the union of all the sets in H. DEFINITION. Suppose F and G are graphs with X-projection [0, 1]. The statement that F is dense (c-dense) along G means that if [a, b] is a subinterval of [0, 1], then there is a point (are c-many points) of intersection of F and G with abscissa in [a, b]. In this paper, the following three theorems will be proved:
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