Measurement topology and characterizations of continuous posets
MAO Xu-xin1, XU Luo-shan2
1. College of Sci., Nanjing Univ. of Aeronautics and Astronautics, Nanjing 210016, China
2. School of Math. Sci., Yangzhou Univ., Yangzhou 225002, China
Abstract Some properties of the measurement topology on posets and relations with other intrinsic topologies are given. In terms of the measurement topology, continuity of posets are characterized. A counterexample is constructed to prove that the measurement topology on a completely distributive lattice need not be locally compact, revealing that the measurement topology itself needn’t be continuous.
MAO Xu-xin, XU Luo-shan. Measurement topology and characterizations of continuous posets. Applied Mathematics A Journal of Chinese Universities, 2014, 29(4): 462-466.
