The class of developable topological spaces, which includes the metrizable spaces, has been fundamentally involved in investigations in point set topology. One example is the remarkable edifice of theorems relating to these spaces constructed by R. L. Moore (13). Another is the role played by the developable property in several metrization theorems, including Alexandroff and Urysohn's original solution of the general metrization problem (1).This paper presents an anslysis of the concept of developable space in terms of certain more extensive classes of spaces satisfying the first axiom of countability : spaces with a base of countable order and those having what is here called a θ-base. The analysis is given in the characterizations of Theorems 3 and 4 below.

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The main theorem of this paper characterizes the class of essentially T1 spaces having bases of countable order as those spaces of the class of essentially T1 spaces having primitive bases in which closed sets are sets of interior condensation. In addition we deduce some corollaries of this theorem, derive some other characterizations, and prove a lemma concerning primitive sequences which is a key to the proof of the main theorem and has other applications.

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