ISSN:
1588-2829
Schlagwort(e):
Primary 54D99
;
Secondary 54D10
;
54D15
;
T i -distinct point (i=0, 1, 2), regularity
;
normality
;
R D -separation axioms
;
paracompact
Quelle:
Springer Online Journal Archives 1860-2000
Thema:
Mathematik
Notizen:
Abstract In a topological spaceX, a T2-distinct pointx means that for anyy∈X x≠y, there exist disjoint open neighbourhoods ofx andy. Similarly, T0-distinct points and T1distinct points are defined. In a Ti-distinct point-setA, we assume that eachx∈A is a T i -distinct point (i=0, 1, 2). In the present paper some implications of these notions which ‘localize’ the T i -separation axioms (i=0, 1, 2) requirement, are studied. Suitable variants of regularity and normality in terms of T2-distinct points are shown hold in a paracompact space (without the assumption of any separation axioms). Later T0-distinct points are used to give two characterizations of the R D -axiom.1 In the end, some simple results are presented including a condition under which an almost compact set is closed and a result regarding two continuous functions from a topological space into a Hausdorff space is sharpened. A result which relates a limit pointv to an ω-limit point is stated.
Materialart:
Digitale Medien
URL:
http://dx.doi.org/10.1007/BF02018917
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