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Order-homomorphism and Extension of Consistently Connected Continuous Domains

Dongming Liu, Guanghao Jiang

Abstract



Firstly, we will give the definition of consistently connected ideal and study its basic properties. Secondly, we introduce consistently connected minimal set and consistently connected base on the consistently connected complete posets, and we will give their some equivalent characterizations. Finally, we also will introduce the order-homomorphism of consistently connected continuous domains and obtain its some good properties. On this
basic, we will give a relevant extension theorem at last.

Keywords


consistently connected ideal; consistently connected minimal set; consistently connected base; consistently connected continuous Domain; order-homomorphism.

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