The topology of a topological sum of orderable spaces is induced by the union of two order topologies
Keywords:
orderable, suborderable, topological sum, ordered setAbstract
It is known that the subspace $X=(0,1) \cup\{2\}$ in the real line $\mathbb{R}$ is the topological sum of the ordered subspaces $(0,1)$ and $\{2\}$ of $\mathbb{R}$ which is not orderable. In this paper, we prove that the topology of a topological sum of orderable spaces is induced by the union of two order topologies.
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