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arXiv · 1509.08659

A note on generators of the endomorphism semigroup of an infinite countable chain

Ilinka Dimitrova·Vítor H. Fernandes·Jörg Koppitz
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Abstract

In this note, we consider the semigroup $O(X)$ of all order endomorphisms of an infinite chain $X$ and the subset $J$ of $O(X)$ of all transformations $\alpha$ such that $|Im(\alpha)|=|X|$. For an infinite countable chain $X$, we give a necessary and sufficient condition on $X$ for $O(X) = \langle J \rangle$ to hold. We also present a sufficient condition on $X$ for $O(X) = \langle J \rangle$ to hold, for an arbitrary infinite chain $X$.

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Ilinka Dimitrova, Vítor H. Fernandes, Jörg Koppitz. 2015-09-29. A note on generators of the endomorphism semigroup of an infinite countable chain. https://doi.org/10.1142/s0219498817500311

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