Abstract
In this paper, we calculate the number, up to homeomorphism, of a certain type of dendrites of order 3. This problem arises out of an attempt to characterize certain congruences of S(X), the semigroup of continuous self maps of a topological space X. The dendrites D under consideration are those which satisfy the condition that for each branch point b of D at least one of the components of D — {b} is either an arc or a triod. To facilitate our calculation we first show that each of such dendrites is homeomorphic to one of an apparently more restricted class. We then classify the dendrites into homeomorphism classes and finally calculate the number of such classes.
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