R1-Topological Spaces1
- 1 January 1966
- journal article
- Published by Canadian Mathematical Society in Canadian Mathematical Bulletin
- Vol. 9 (4) , 521-523
- https://doi.org/10.4153/cmb-1966-065-4
Abstract
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.Keywords
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