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Topological realizations of groups in Alexandroff spaces Chocano Feito, Pedro José Alonso Morón, Manuel Romero Ruiz Del Portal, Francisco This is a pre-print of an article published in Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas . The final authenticated version is available online at: https://doi.org/10.1007/s13398-020-00964-7”. Given a group G, we provide a constructive method to get infinitely many (non-homotopy-equivalent) Alexandroff spaces, such that the group of autohomeomorphisms, the group of homotopy classes of self-homotopy equivalences and the pointed version are isomorphic to G. As a result, any group G can be realized as the group of homotopy classes of self-homotopy equivalences of a topological space X, for which there exists a CW complex K(X) and a weak homotopy equivalence from K(X) to X. 2023-06-17T08:56:07Z 2023-06-17T08:56:07Z 2020-11-23 journal article Chocano Feito, P. J., Alonso Morón, M. y Romero Ruiz Del Portal, F. «Topological Realizations of Groups in Alexandroff Spaces». Revista de La Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, vol. 115, n.o 1, enero de 2021, p. 25. DOI.org (Crossref), https://doi.org/10.1007/s13398-020-00964-7. 1578-7303 10.1007/s13398-020-00964-7 https://hdl.handle.net/20.500.14352/7571 https://doi.org/10.1007/s13398-020-00964-7 https://link.springer.com/article/10.1007/s13398-020-00964-7 eng (MTM2015-63612-P; PGC2018-098321-B-100; BES-2016-076669) open access Springer