LAUSR

Abstract Straight spaces are metric spaces X having the property that for a cover X = A ∪ B by two closed sets, any continuous function f : X → R is uniformly continuous provided it is so on each of the sets A and B (it is actually called ‘2-straight’ but is easier to deal with [8] ). In this paper we consider this nice idea and instead of uniformly continuous functions, we consider Cauchy regular functions [18] and ward continuous functions [12] , as these classes of functions strictly lie between the classes of continuous and uniformly continuous functions. In the process we obtain two natural variations of straightness which we name pre-straight and W-straight spaces respectively. We primarily investigate these notions along with another notion called pre ( ⁎ ) -straight which actually helps us to obtain a better understanding of the relation-ship between the notions of straight and pre-straight ness.