s₂ -代数超连续偏序集

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s2 -AlgebraicSupercontinuousPoset

Wu Changzhong

(Anhui Vocational and Technical CollgeofPostsand Telecommunications,Hefei23oo31,China)

【Abstract】 This paper investigates several properties of s2- algebraically supercontinuous posets (partially ordered sets). First, the author introduces the definition of s2 bases for s2. supercontinuous posets and provide equivalent characterizations of such s2 -bases.Next, theauthor establishes several equivalent conditionsfor s2- algebraicallysupercontinuous posets.Finally,by utilizing property *,the author derives a sufficient condition under which a s2 set forms atopology.

【Key words】 s2. : supercontinuous poset; s2- algebraic supercontinuous poset; s2. base; s2 set

[中图分类号]0153.1 [文献标识码]A

[文章编号]1674-3229(2025)03-0014-05

0 引言

偏序集的超连续性一直是偏序集研究的重要方向之一，利用集合的上确界可以定义超连续格，且连续的上半格与超连续格等价[1-3]。（剩余15428字）