Abstract
The Isbell Zigzag Theorem for pomonoids was first proved by Sohail Nasir in 2013. In this paper we give a short proof of the Zigzag Theorem for commutative pomonoids. We also prove that certain submonoids of full transformation monoid on a non empty set are closed in the containing monoids. In particular we prove that the monoid of all surjective mappings and the pomonoid of all monotone mappings are absolutely closed.
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Ahanger, S.A., Shah, A.H. On zigzag theorem for commutative pomonoids and certain closed and absolutely closed monoids and pomonoids. Beitr Algebra Geom 61, 9–21 (2020). https://doi.org/10.1007/s13366-019-00452-z
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DOI: https://doi.org/10.1007/s13366-019-00452-z