# Countable Successor Ordinals as Generalized Ordered Topological Spaces Academic Article

•
• Overview
•

### abstract

• Abstract: A topological space $L$ is called a linear ordered topological space (LOTS) whenever there is a linear order $\leq$ on $L$ such that the topology on $L$ is generated by the open sets of the form $(a, b)$ with $a< b$ and $a, b\in L\cup\{-\infty,+\infty\}$. A topological space $X$ is called a generalized ordered space (GO-space) whenever $X$ is topologically embeddable in a LOTS. Main Theorem: Let $X$ be a Hausdorff topological space. Assume that any continuous image of $X$ is a GO-space. Then $X$ is …

• May 17, 2016