Yazar "Onat, Mehmet" seçeneğine göre listele

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    On compactifications of an orbit space
    (Univ Nis, Fac Sci Math, 2024) Onat, Mehmet
    One of the important research topics in the theory of topological transformation groups is to examine the relationships between the topological properties of a G-space X and the orbit space X / G . In [7], Antonyan and Smirnov studied the relationship between the Stone-Cech compactification of a completely regular space and the Stone-Cech compactification of the orbit space. A similar study was done for the Hewitt realcompactification in [8, 14]. In this paper, we obtain that the c-realcompactification of the orbit space X / G is homeomorfic to the orbit space of the c-realcompactification of X , when G is a finite discrete group and X is a completely regular G-space. We will also show a similar result for almost realcompactification.
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    The Borsuk-Ulam Type Theorems for Finite-Dimensional Compact Group Actions
    (Springer Singapore Pte Ltd, 2022) Onat, Mehmet
    Clapp and Puppe (J. Reine Angew Math 418:1-29, 1991) proved that, if G is a torus or a p-torus, X is a path-connected G-space and Y is a finite-dimensional G-CW complex without fixed points, under certain cohomological conditions on X and Y, there is no equivariant map from X to Y. Also, Biasi and Mattos (Bull Braz Math Soc New Ser 37:127-137, 2006) proved that, again under certain cohomological conditions on X and Y, there is no equivariant map from X to Y provided that G is a compact Lie group and X, Y are path-connected, paracompact, free G-spaces. In this paper, our objective is to generalize these results for the actions of finite-dimensional pro-tori and compact groups, respectively.
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    The Hewitt realcompactification of an orbit space
    (Tubitak Scientific & Technological Research Council Turkey, 2020) Eyidogan, Sadik; Onat, Mehmet
    In this paper, we show that the statement in the study of Srivastava (1987) holds also for the Hewitt realcompactification. The mentioned statement showed that when the action of a finite topological group on a Tychonoff space is given, the Stone-Cech compactification of the orbit space of the action is the orbit space of the Stone-Cech compactification of the space. As an application, we show that Srivastava's result can be obtained using the main theorem of the present study.