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Abstract
The Comfort order is known as an order on the Stone–Cech compactification of a discrete semigroup. This order has an important role in the investigation of the structure of the Stone–Cech compactification. Let S be a semitopological semigroup. The collection of all bounded continuous functions on S, such that its set of right translations is relatively compact in \(\mathcal {CB}(S)\), equipped by the topology of pointwise convergence on S, is denoted by Lmc(S). The spectrum of Lmc(S) is called Lmc-compactification and has been reconstructed as a space of z-filters. In this paper, the comfort order on Lmc-compactification of a semitopological semigroup is defined and studied in relation to Lmc-compactification.
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