Transitivity is neither hereditary nor finitely productive |
| |
Authors: | Hans-Peter A Künzi |
| |
Institution: | Mathematisches Institut, Universität Bern, Sidlerstrasse 5, 3012 Bern, Switzerland |
| |
Abstract: | We construct a transitive space that is the union of two subspaces homeomorphic to the (non-transitive) Kofner plane. Moreover, we show that the product of two transitive spaces need not be transitive. Finally, we observe that results of E.K. van Douwen establish that, under b = c, there exists a locally countable locally compact non-transitive zero-dimensional space. It follows that under b = c neither a locally transitive nor a compact space need be transitive. |
| |
Keywords: | Primary 54D18 54B05 54B10 transitive product neighbor net subspace orthocompact |
本文献已被 ScienceDirect 等数据库收录! |
|