AN EXAMPLE CONCERNING LOTS WI'fH all-BASES

In 1966 Worrell and Wicke [WW] introduced the concept of a 8-base as a generalization of developability. In 1967 Bennett [B] introduced another generalization of developablel spaces, namely, quasi-developable spaces. In 1971 Bennett and Lutzer [BL] showed that the concept of a 8-base and a quasi-developable space are the same. In 1974 Aull [A] introduced and studied spaces with o8-bases, an obvious generalization of spaces with 8-bases. In [B] it was shown that a LOTS with a 8-base has a2 point-countable base and an example was given of a LOTS with a point-countable base that did not have a 8-base. In this note an example of a LOTS with a o8-base that does not have a point-countable base is given. Let N, P and Q denote the set of natural numbers, the set of irrational numbers and the set of rational number