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Z-exact Posets and Quasi Z-exact Posets

Author: ZhangChunBo
Tutor: XuXiaoQuan
School: Jiangxi Normal University
Course: Basic mathematics
Keywords: Z-complete posets Z-exact posets Z-minimal sets quasi Z-exact posets Z-meet exact posets quasi Z-algebraic exact posets
CLC: O153.1
Type: Master's thesis
Year: 2008
Downloads: 4
Quote: 0
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Abstract


In this paper, for a general subset Z, we define the concept of Z-minimalsets, Z-exact posets, quasi Z-exact posets, Z-meet exact posets and quasi Z-algebraic exact posets. And the equivalent characterizations between the mapping preserving the Z-minimal sets and the mapping preserving <<Z-ω and the Z-exact posets are discussed and we also study some properities of Z-exact posets. The corresponding extension theorem is proved. For the general function space of Z-exact posets, we discuss its some properties. The characterizations of quasi Z-exact posets, Z-meet exact posets and quasi Z-algebraic exact posets are given. And their some characterization are discussed. We prove that Z is the property M of Rudin subset system and P is Z- exact posets, then P is quasi Z-exact posets. We prove that Z is finite join Rudin subset system and P is quasi Z-exact posets, then （P,λZ（P）） is Hausdroff space. We prove that P is Z-meet exact posets andλZ（P） is Huasdorff, then P is weakly Z-exact posets. Also we prove that P is quasi Z-algebraic exact posets, then P is quasi Z-exact posets.

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CLC: > Mathematical sciences and chemical > Mathematics > Algebra,number theory, portfolio theory > Abstract algebra ( Algebra ) > Collection of partial order and lattice theory
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