Monotone normality and neighborhood assignments |
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Authors: | Hang Zhang Wei-Xue Shi |
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Institution: | a College of Mathematics, Sichuan University, Chengdu 610064, China b Department of Mathematics, Nanjing University, Nanjing 210093, China |
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Abstract: | We prove that every neighborhood assignment for a monotonically normal space has a kernel which is homeomorphic to some subspace of an ordinal. As a corollary, every monotone neighborhood assignment for a monotonically normal space has a discrete kernel, which gives a partial answer to a question posed in Buzyakova et al. (2007) 5]. We also give an example of a regular space which has a neighborhood assignment with no kernels homeomorphic to any subspace of an ordinal. |
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Keywords: | Monotonically normal Neighborhood assignment Dually discrete D-space |
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