Countable Successor Ordinals as Generalized Ordered Topological Spaces Academic Article uri icon

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 …

publication date

  • May 17, 2016