{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,26]],"date-time":"2026-02-26T20:22:36Z","timestamp":1772137356710,"version":"3.50.1"},"reference-count":40,"publisher":"Steklov Mathematical Institute","issue":"2","license":[{"start":{"date-parts":[[2021,2,1]],"date-time":"2021-02-01T00:00:00Z","timestamp":1612137600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/iopscience.iop.org\/page\/copyright"},{"start":{"date-parts":[[2021,2,1]],"date-time":"2021-02-01T00:00:00Z","timestamp":1612137600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/iopscience.iop.org\/info\/page\/text-and-data-mining"}],"funder":[{"name":"Austrian Science Fund","award":["P31591"],"award-info":[{"award-number":["P31591"]}]}],"content-domain":{"domain":["iopscience.iop.org"],"crossmark-restriction":false},"short-container-title":["Sb. Math."],"published-print":{"date-parts":[[2021,2,1]]},"abstract":"Abstract<\/jats:title>\n \n Let\n \n \n \n <\/jats:tex-math>\n \n <\/jats:inline-formula>\n and\n \n \n \n <\/jats:tex-math>\n \n <\/jats:inline-formula>\n be locally compact groups with fixed two-sided invariant Haar measures. A polyhomomorphism\n \n \n \n <\/jats:tex-math>\n \n <\/jats:inline-formula>\n is a closed subgroup\n \n \n \n <\/jats:tex-math>\n \n <\/jats:inline-formula>\n with fixed Haar measure, whose marginals on\n \n \n \n <\/jats:tex-math>\n \n <\/jats:inline-formula>\n and\n \n \n \n <\/jats:tex-math>\n \n <\/jats:inline-formula>\n are dominated by the Haar measures on\n \n \n \n <\/jats:tex-math>\n \n <\/jats:inline-formula>\n and\n \n \n \n <\/jats:tex-math>\n \n <\/jats:inline-formula>\n . A polyhomomorphism can be regarded as a multi-valued map sending points to sets equipped with \u2018uniform\u2019 measures. For two polyhomomorphisms\n \n \n \n <\/jats:tex-math>\n \n <\/jats:inline-formula>\n and\n \n \n \n <\/jats:tex-math>\n \n <\/jats:inline-formula>\n there is a well-defined product\n \n \n \n <\/jats:tex-math>\n \n <\/jats:inline-formula>\n . The set of polyhomomorphisms\n \n \n \n <\/jats:tex-math>\n \n <\/jats:inline-formula>\n is a metrizable compact space with respect to the Chabauty-Bourbaki topology and the product is separately continuous. A polyhomomorphism\n \n \n \n <\/jats:tex-math>\n \n <\/jats:inline-formula>\n determines a canonical operator\n \n \n \n <\/jats:tex-math>\n \n <\/jats:inline-formula>\n , which is a partial isometry up to a scalar factor. For example, we consider locally compact linear spaces over finite fields and examine the closures of groups of linear operators in semigroups of polyhomomorphisms.\n <\/jats:p>\n Bibliography: 40 titles.<\/jats:p>","DOI":"10.1070\/sm9412","type":"journal-article","created":{"date-parts":[[2020,11,13]],"date-time":"2020-11-13T16:25:48Z","timestamp":1605284748000},"page":"185-210","update-policy":"https:\/\/doi.org\/10.1088\/crossmark-policy","source":"Crossref","is-referenced-by-count":1,"title":["Polyhomomorphisms of locally compact groups"],"prefix":"10.4213","volume":"212","author":[{"given":"Yu. A.","family":"Neretin","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"2731","reference":[{"key":"MSB_212_2_185bib1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-40409-6","volume":"115","author":"Hewitt","year":"1963","journal-title":"Grundlehren Math. 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