Geodesic
R1-Topological Spaces1
Canadian mathematical bulletin, Tome 9 (1966) no. 4, pp. 521-523

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In his paper ′′Indexed systems of neighborhoods for general topological spaces′′ (Amer. Math. Monthly 68, (1961), 886–893), A.S. Davis defined a hierarchy of what he called regularity axioms. The R1 -axiom is independent of both T0 and T1, but is strictly weaker than T2. In this note, we propose to study the properties of the spaces satisfying the R1 -axiom. In particular, we will show that in many well-known results, the hypothesis can be weakened from T2 to R1, which is part of our motivation in studying R1 -spaces. 
Murdeshwar, M.G.; Naimpally, S.A. R1-Topological Spaces1. Canadian mathematical bulletin, Tome 9 (1966) no. 4, pp. 521-523. doi: 10.4153/CMB-1966-065-4
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     title = {R1-Topological {Spaces1}},
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     year = {1966},
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     doi = {10.4153/CMB-1966-065-4},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1966-065-4/}
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