JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2016, Vol. 51 ›› Issue (4): 112-117.doi: 10.6040/j.issn.1671-9352.0.2015.430

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The supremum and infimum of partially ordered objects in a topos

LU Tao1, WANG Xi-juan2*, HE Wei3   

  1. 1. School of Mathematical Sciences, Huaibei Normal University, Huaibei 235000, Anhui, China;
    2. Department of Mathematics, Nanjing University, Nanjing 210097, Jiangsu, China;
    3. School of Mathematical Sciences, Nanjing Normal University, Nanjing 210097, Jiangsu, China
  • Received:2015-10-15 Online:2016-04-20 Published:2016-04-08

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Abstract: The concepts of supremum and infimum which are common generalizations of lattice theory is introduced, and some well-known lattice theory into an arbitrary topos is lifted. The main result that an object in a topos is a complete partially ordered object if and only if its general subset has supremum and infimum is obtianed.

Key words: partially ordered object, supremum(infimum), topos, complete partially ordered object

CLC Number: 

  • O189.11
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[1] LU Tao, WANG Xi-juan, HE Wei. The operator theory on complete partially ordered objects in a topos [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(2): 64-71.
[2] LU Tao, WANG Xi-juan, HE Wei. An equivalent characterization of the choice axiom in a Topos [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2015, 50(12): 54-57.
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