### The operator theory on complete 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 Science, Nanjing Normal University, Nanjing 210097, Jiangsu, China
• Received:2015-10-15 Online:2016-02-16 Published:2016-03-11

Abstract: The concept of the projective operators between complete partially ordered objects in a topos is investigated. The characterizations of the closure operator and the kernel operator in a topos are given, which are common generalizations of the classical lattice theory.

CLC Number:

• O189.11
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 [1] LU Tao, WANG Xi-juan, HE Wei. The supremum and infimum of partially ordered objects in a topos [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(4): 112-117. [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. [3] ZHANG Yan-xia, LI Sheng-gang*, XIAN Lu. Products, sums, and quotients of M-closure spaces [J]. J4, 2010, 45(4): 74-76.
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