Abstract
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 + e), e > 0} of half-open intervals, and if x ∈ SP, then a base of neighborhoods of x is the family {(x − e, x], e > 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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