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- Title
On a Homeomorphism between the Sorgenfrey Line <italic>S</italic> and Its Modification <italic>S</italic><sub><italic>P</italic></sub>.
- Authors
Khmyleva, T. E.; Sukhacheva, E. S.
- Abstract
A topological space <italic>S</italic><italic>P</italic>, which is a modification of the Sorgenfrey line <italic>S</italic>, is considered. It is defined as follows: if <italic>x</italic> ∈ <italic>P</italic> ⊂ <italic>S</italic>, then a base of neighborhoods of <italic>x</italic> is the family {[<italic>x</italic>, <italic>x</italic> + <italic>ε</italic>), <italic>ε</italic> > 0} of half-open intervals, and if <italic>x</italic> ∈ <italic>S</italic><italic>P</italic>, then a base of neighborhoods of <italic>x</italic> is the family {(<italic>x</italic> − <italic>ε</italic>, <italic>x</italic>], <italic>ε</italic> > 0}. A necessary and sufficient condition under which the space <italic>S</italic><italic>P</italic> is homeomorphic to <italic>S</italic> is obtained. Similar questions were considered by V. A. Chatyrko and I. Hattori, who defined the neighborhoods of <italic>x</italic> ∈ <italic>P</italic> to be the same as in the natural topology of the real line.
- Subjects
CONDENSATION; BAIRE spaces; HOMEOMORPHISMS; ORDINAL numbers; TOPOLOGY
- Publication
Mathematical Notes, 2018, Vol 103, Issue 1/2, p259
- ISSN
0001-4346
- Publication type
Article
- DOI
10.1134/S0001434618010273