Partially ordered metric spaces produced by T₀-quasi-metrics

详细信息    查看全文

• 作者：Yaé ; Ulrich Gaba ^{gabayae2@gmail.com" class="auth_mail" title="E-mail the corresponding author} ; Hans-Peter A. Kü ; nzi ; ^{hans-peter.kunzi@uct.ac.za" class="auth_mail" title="E-mail the corresponding author}
• 关键词：54F05 ; 54E15 ; 54E35 ; 06A06 ; 06F30 ; 06F15
• 刊名：Topology and its Applications
• 出版年：2016
• 出版时间：1 April 2016
• 年：2016
• 卷：202
• 期：Complete
• 页码：366-383
• 全文大小：490 K

文摘

We continue our investigation on those (partially) ordered metric spaces class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S016686411600064X&_mathId=si1.gif&_user=111111111&_pii=S016686411600064X&_rdoc=1&_issn=01668641&md5=f4b70b59248e267ac3d59ff0763e1328" title="Click to view the MathML source">(X,m,≤)class="mathContainer hidden">class="mathCode">$(X,m,\le )$ for which there exists a class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S016686411600064X&_mathId=si113.gif&_user=111111111&_pii=S016686411600064X&_rdoc=1&_issn=01668641&md5=c54e3a934a6afb94b08ef836d0430fad" title="Click to view the MathML source">T₀class="mathContainer hidden">class="mathCode">$T_0$-quasi-metric d on X   such that class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S016686411600064X&_mathId=si3.gif&_user=111111111&_pii=S016686411600064X&_rdoc=1&_issn=01668641&md5=516fed0468b3a758f6ad7d1b5f14e930" title="Click to view the MathML source">sup⁡{d,d⁻¹}=mclass="mathContainer hidden">class="mathCode">$\sup \{d,d^{-1}\}=m$ and for any class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S016686411600064X&_mathId=si383.gif&_user=111111111&_pii=S016686411600064X&_rdoc=1&_issn=01668641&md5=2d0e240755f0e63936c747732a9a9a9d" title="Click to view the MathML source">x,y∈Xclass="mathContainer hidden">class="mathCode">$x,y\in X$ we have that class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S016686411600064X&_mathId=si387.gif&_user=111111111&_pii=S016686411600064X&_rdoc=1&_issn=01668641&md5=dc35cf01ad0bb62c65ee9d59bcb08155" title="Click to view the MathML source">x≤yclass="mathContainer hidden">class="mathCode">$x\le y$ if and only if class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S016686411600064X&_mathId=si6.gif&_user=111111111&_pii=S016686411600064X&_rdoc=1&_issn=01668641&md5=e0bc1d0e7dab7740b0fe131c5186a8c7" title="Click to view the MathML source">d(x,y)=0class="mathContainer hidden">class="mathCode">$d(x,y)=0$. In particular such partially ordered metric spaces are determined (in the sense of Nachbin) by a class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S016686411600064X&_mathId=si113.gif&_user=111111111&_pii=S016686411600064X&_rdoc=1&_issn=01668641&md5=c54e3a934a6afb94b08ef836d0430fad" title="Click to view the MathML source">T₀class="mathContainer hidden">class="mathCode">$T_0$-quasi-uniformity with a countable base.

We show that the compatibility conditions obtained in an earlier study between partial order and metric on the investigated spaces X become more transparent when additional compatibility conditions between metric and partial order with appropriate algebraic operations on X are assumed to hold.