We present an example of a separable metrizable topological group G having the property that no remainder of it is (topologically) homogeneous.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ba63-1-8, author = {A. V. Arhangel'skii and J. van Mill}, title = {Nonhomogeneity of Remainders, II}, journal = {Bulletin of the Polish Academy of Sciences. Mathematics}, volume = {63}, year = {2015}, pages = {67-71}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba63-1-8} }
A. V. Arhangel'skii; J. van Mill. Nonhomogeneity of Remainders, II. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 63 (2015) pp. 67-71. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba63-1-8/