On a homeomorphism between the Sorgenfrey line S and its modification Sp E. S. Sukhacheva, T. E. Khmyleva
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ArticleContent type: Текст Media type: электронный Subject(s): гомеоморфизм | ординалы | нигде не плотные множества | Бэра пространство | Зоргенфрея прямая | точка конденсацииGenre/Form: статьи в журналах Online resources: Click here to access online
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Mathematical notes Vol. 103, № 2. P. 259-270Abstract: A topological space S P , which is a modification of the Sorgenfrey line S, is considered. It is defined as follows: if x ∈ P ⊂ S, then a base of neighborhoods of x is the family {[x, x + ε), ε > 0} of half-open intervals, and if x ∈ SP, then a base of neighborhoods of x is the family {(x − ε, x], ε > 0}. A necessary and sufficient condition under which the space S P is homeomorphic to S is obtained. Similar questions were considered by V. A. Chatyrko and I. Hattori, who defined the neighborhoods of x ∈ P to be the same as in the natural topology of the real line.
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A topological space S P , which is a modification of the Sorgenfrey line S, is considered. It is defined as follows: if x ∈ P ⊂ S, then a base of neighborhoods of x is the family {[x, x + ε), ε > 0} of half-open intervals, and if x ∈ SP, then a base of neighborhoods of x is the family {(x − ε, x], ε > 0}. A necessary and sufficient condition under which the space S P is homeomorphic to S is obtained. Similar questions were considered by V. A. Chatyrko and I. Hattori, who defined the neighborhoods of x ∈ P to be the same as in the natural topology of the real line.
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