A study of acyclically monotonically \(T_2\) spaces. (English) Zbl 1137.54317
Summary: In this paper, we shall prove that acyclically monotonically \(T_2\) is a properly hereditary property, and every metric space is an acyclically monotonically \(T_2\) space. Moreover, we shall give a characterization of acyclically monotonically \(T_2\). Also, some open problems and conjectures concerning acyclically monotonically \(T_2\) spaces and their relation with strongly monotonically \(T_2\) space will be given.
MSC:
54D10 | Lower separation axioms (\(T_0\)–\(T_3\), etc.) |
54E35 | Metric spaces, metrizability |
54G20 | Counterexamples in general topology |