Relative separation properties
Abstract
Relative topological properties theory is an important branch of research in general topology because, among other applications, it helps to know how is a space Y located in a superspace X. Besides, a relative topological property generalize the global topological property from which it comes, in the sense that if $Y$ is equal to $X$, the relative property and the global property coincide. In the present paper, we make a thorough study of several version that emerge from the separations axioms T1, T2, T3 andT4. Specifically, of the concepts defined, we provide examples that guarantee its independence, we establish characterizations of them and we give conditions under which there are coincidences.
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References
Arhangel’skii, A. V. (1996). Relative topological properties and relative topological spaces. Topology Appl., 70:87–99.
Arhangel’skii, A. V. (2002). Relative normality and dense subspaces. Topology Appl., 123:27–36.
Arhangel’skii, A. V. and Genedi, H. M. M. (1989). Beginnings of the theory of relative topological properties. General Topology Spaces and Mappings (MGU, Moscow) (en ruso), 70:3–48.
Arhangel’skii, A. V. and Tartir, J. (1996). A characterization of compactness by a relative separation property. Question and Answers in General Topology, 14:49–52.
D´ıaz-Reyes, J., Mart´ınez-Ruiz, I., and Ram´ırez-P´aramo, A. (2019). Relative topological properties of hyperspaces. Mathematica Slovaca, 69:675–684.
Engelking, R. (1989). General topology. Heldermann Verlag Berlin, University of Michigan.
Grabner, E., Grabner, G., Miyazaki, K., and Tartir, J. (2005). Relative star normal type. Topology Appl., 153:874–885.
Sarsak, M. S. and Hdeib, H. Z. (2010). Relative strongly normal and relative normal subspaces. International Mathematical Forum, 5:579–586.
