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On a generalization of Hausdorff space [PDF]
International Journal of Mathematics and Mathematical Sciences, 1986 Here, a new separation axiom as a generalization of that of Hausdorff is introduced. Its simple consequences and relations with some other known separation axioms are studied. That a non-indiscrete topological group satisfies this axiom is shown.
Tapas Dutta
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Canadian Mathematical Bulletin, 1966 It is well-known that in a Hausdorff space, a sequence has at most one limit, but that the converse is not true. The condition that every sequence have at most one limit will be called the semi-Hausdorff condition. We will prove that the semi-Hausdorff condition is strictly stronger than the T1 -axiom and is thus between the T1 and T2 axioms.
M.G. Murdeshwar, S.A. Naimpally
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Optical hausdorff quantum energy of spherical magnetic particles [PDF]
Scientific ReportsIn this article, a new approach for spherical magnetic curves under the spherical system in spherical space is given. Firstly, the Hausdorff derivative of the Lorentz spherical magnetic fields $$\phi ( \varvec{\beta }),$$ $$\phi \left( \varvec{t}\right) ,
Talat Körpinar +4 more
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On minimal Hausdorff spaces [PDF]
Journal of the Australian Mathematical Society, 1977 AbstractIn this paper, several characterizations of minimal Hausdorff spaces are given.
James E. Joseph
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Characterizations of Minimal Hausdorff Spaces [PDF]
Proceedings of the American Mathematical Society, 1976 Two new characterizations of minimal Hausdorff spaces are given along with some relating properties and examples.
James E. Joseph
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A Connected Countable Hausdorff Space [PDF]
Proceedings of the American Mathematical Society, 1953 In Math. Ann. vol. 94 (1925) pp. 262-295, Urysohn gave an example of a connected Hausdorff space with only countably many points. Here is another. EXAMPLE 1. The points of the space are the rational points in the plane on or above the x-axis. If (a, b) is such a point and e>0, (a, b)+{(r, 0)1 either 1r-(a+b/31I2)|
R. Bing
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On countable connected Hausdorff spaces in which the intersection of every pair of connected subsets in connected [PDF]
International Journal of Mathematics and Mathematical Sciences, 1998 We prove that a countable connected Hausdorff space in which the intersection of every pair of connected subsets is connected, cannot be locally connected, and also that every continuous function from a countable connected, locally connected Hausdorff ...
V. Tzannes
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Embeddings in minimal Hausdorff spaces [PDF]
Proceedings of the American Mathematical Society, 1983 We show that not every semiregular space is embeddable as an open and dense set of some minimal Hausdorff space. Also a space is constructed for which it is not decidable in Z.F.C whether such an embedding exists.
Johannes Vermeer
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Topology and its Applications, 1992 The author's introduction: ``Until about 1950 it seemed that, with few exceptions, topologists had a theorem which said ``all spaces are Hausdorff''. Early examples of the study of non-Hausdorff spaces are provided by the Sierpinski space, \textit{P. Alexandroff's} ``diskrete Räume'' [Mat. Sb. = Rec. Math. Moscou, N.S. 2, 501-518 (1937; Zbl 0018.09105)]
Ivan L. Reilly
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A characterization of minimal Hausdorff spaces [PDF]
Proceedings of the American Mathematical Society, 1976 This paper gives a characterization of minimal Hausdorff spaces.
Larry L. Herrington, Paul E. Long
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