There is no universal countable random-free graph
We consider embeddings between infinite graphs. In particular, We establish that there is no universal element in the class of countable graphs into which the random graph is not embeddable.
math.CO↗
arXiv subjects
Masasi Higasikawa
Publications and source records attributed to Masasi Higasikawa.
Non-productive duality properties of topological groups
We address two properties for Abelian topological groups: ``every closed subgroup is dually closed'' and ``every closed subgroup is dually embedded.'' We exhibit a pair of topological groups such that each has both of the properties and the product has neither, which refutes a remark of N. Noble. These examples are the additive group of integers topologized with respect to a convergent sequence as investigated by E.G. Zelenyuk and I.V. Protasov. The proof for the product relies on a theorem on exponential Diophantine equations.
math.GN↗
Topological groups with several disconnectedness
We investigate some properties of topological groups related to disconnectedness or Archimedeanness. We prove or disprove the preservation of those under operations as subgroups, quotients, products, etc. Characterizations of non-Archimedeanness are obtained by using embedding into universal groups. We also clarify the differences between the properties by constructing miscellaneous Polish groups.
math.GN↗