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On the Smallest Base of the Stone Space
作者姓名:白瑞蒲
作者单位:Dept. of Math.,Hebei University,Baoding,071002
摘    要:51.IntroductionandDefinitionInl]ithadbeenprovedthat:ifadistributivelatticeLpossessesthesmal1estsetofgen-eratingelements,thenLsatisfiesjointinfinitelydistributivelaw.AndinL2jproved:acom-pletelydistributivelatticepossessesminimalsetofgeneratingelements,thenLisastrongalge-bra.lnthispaper,theconceptofthesetofgeneraingelementsisdifferentfrom1j.Wewillsolvetheexistenceproblemoftheminimalsetofgeneratingelementsbyuseofthetopologicalrepresentation.Firstwedefinethesmallestbase,strongopensetinthetopol…

关 键 词:Stone空间  最小基  强开集

On the Smallest Base of the Stone Space
Bai Ruipu.On the Smallest Base of the Stone Space[J].Chinese Quarterly Journal of Mathematics,1997,12(1):91-94.
Authors:Bai Ruipu
Abstract:In this paper,first we define the concept of strong open set for topological space. Then we prove: 1 ) a distributive lattice L possesses the smallest set of generating elements if and only if the Stone space (L) of L possesses a smallest base constructed by strong open sets; 2) a Bollean lattice B possesses the smallest set of generating elements if and only if B is a finite Boolean lattice.
Keywords:Stone space  strong open set  smallest base: smallest set of generating elements
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