The object of this paper is to give some examples of functions which are peculiar with respect to continuity and neighborliness, and also to show that there exist point properties (of functions) with respect to which no function can be peculiar. One such point property, namely that of cliquishness of a junction as defined here is a natural generalization of continuity and neighborliness, but yields results which are quite different from those which hold for continuous or neighborly functions. This property of cliquishness reduces to the property of neighborly' as defined by Bledsoe3 for the case when the domain of definition of the function is an interval (a,b) and the range of the function is a metric space.
Proceedings of the Iowa Academy of Science
© Copyright 1952 by the Iowa Academy of Science, Inc.
Thielman, H. P.
Proceedings of the Iowa Academy of Science, 59(1), 338-343.
Available at: https://scholarworks.uni.edu/pias/vol59/iss1/41