mycoreobjectrosdok_document_0000028047rosdok_document_0000028047rosdokdocumentrosdok_derivate_00002299512026-10-23T08:48:09.301Z2026-10-23T08:37:46.224ZeditorKEeditorKEpublished1rosdok_derivate_0000229951truetruederivate_types:fulltextVolltextfulltextwf_edit_epub wf_register_epubstate:publishedstate:publishedveröffentlichtpublishedrosdok_id000059101987412443Oau2026-10-232026-10-23T08:48:05ZrdaConverted from PICA to MODS using Pica2MODS XSLT Transformer 2.14-SNAPSHOT [SCM: "" "" ""] with mode 'DEFAULT'.WorkingpaperOn a nice embedding and the Ascoli theoremBesides some remarks on hit-and-miss hyperspaces and (relative) compactness of unions of (relative) compact sets, and using these together with a natural map from a function space between topological spaces into a function space between their Vietoris hyperspaces, we derive Ascoli-like theorems for some set-open topologies, nearly related to the compact-open, and mainly for the compact-open topology itself. Some Ascoli-like statements are given, where all requirements are focused on the set of functions, whose (relative) compactness is in question, not on the base spaces.RenéBartsch1970 -VerfasserInaut1242054450009-0009-2471-2874https://purl.uni-rostock.de/rosdok/id00005910urn:nbn:de:gbv:28-rosdok_id00005910-410.18453/rosdok_id00005910510 MathematikMathematisch-Naturwissenschaftliche Fakultätalle Rechte vorbehaltenRechteinhaber Universität Rostockfrei zugänglich (Open Access)Lizenz Metadaten: CC0en1 Online-Ressource (19 Seiten)2003University of Rostock, Institute of MathematicsRostockmonographic20032026Universitätsbibliothek RostockRostock2026Universitätsbibliothek Rostockhttps://purl.uni-rostock.de/rosdok/id00005910René Bartschrosdok_id000058161986139832Odvhttps://purl.uni-rostock.de/rosdok/id00005816Preprints aus dem Institut für Mathematik3255797-803/40003-0004doctype:epubdoctype:epubDokumenttypDocument typedoctype:epub.workingpaperdoctype:epub.workingpaperWorkingpaperworking paperdiniPublType:workingPaper diniPublType2022:WorkingPaperinfo:eu-repo/semantics/workingPaperdocumentdiniPublType2022:WorkingPaperdiniPublType2022:WorkingPaperArbeitspapierWorking paperKDSF (Pu37)SDNB:510SDNB:510510 Mathematik510 Mathematicsinstitution:unirostockinstitution:unirostockUniversität RostockUniversity of RostockUniversität RostockUniversität RostockUni.Rostockhttp://d-nb.info/gnd/38329-6institution:unirostock.mnfinstitution:unirostock.mnfMathematisch-Naturwissenschaftliche FakultätFaculty of Mathematics and Natural SciencesUniversität Rostock. Mathematisch-Naturwissenschaftliche FakultätMathematisch-Natur-<br />wissenschaftliche FakultätUni.Rostock.Fakultaet.MNFhttp://d-nb.info/gnd/2147083-2licenseinfo:worklicenseinfo:workWerkworklicenseinfo:work.rightsreservedlicenseinfo:work.rightsreservedalle Rechte vorbehaltenall rights reserved/creativecommons/r/reserved/0.9/88x31.png[DE-28]Urheberrechtsschutz 1.0$gRights Statements$uhttp://rightsstatements.org/vocab/InC/1.0/http://rightsstatements.org/vocab/InC/1.0/http://rightsstatements.org/vocab/InC/1.0/licenseinfo:depositlicenseinfo:depositVeröffentlichungsgenehmigungpermission to storelicenseinfo:deposit.rightsunirostocklicenseinfo:deposit.rightsunirostockRechteinhaber Universität Rostockrightsholder Rostock Universityaccesscondition:openaccessaccesscondition:openaccessfrei zugänglich (Open Access)open accesshttp://purl.org/coar/access_right/c_abf2OAfreeinfo:eu-repo/semantics/openAccess[DE-28]Open Access$gControlled Vocabulary for Access Rights$uhttp://purl.org/coar/access_right/c_abf2licenseinfo:metadatalicenseinfo:metadataLizenzen für Metadatenlicenseinfo:metadata.cc0licenseinfo:metadata.cc0Lizenz Metadaten: CC0license metadata: CC0/creativecommons/p/zero/1.0/88x31.pnghttps://creativecommons.org/publicdomain/zero/1.0/rfc5646:enrfc5646:enEnglischEnglishengengOn a nice embedding and the Ascoli theoremOn a nice embedding and the Ascoli theoremgnd:124205445orcid:0009-0009-2471-2874gnd:124205445orcid:0009-0009-2471-2874rosdok_document_0000028047-d3976421e49gnd:124205445orcid:0009-0009-2471-2874René BartschRené BartschRené BartschRené BartschRené BartschRostockUniversity of Rostock, Institute of Mathematicsepub.workingpaperhttps://purl.uni-rostock.de/rosdok/id00005910urn:nbn:de:gbv:28-rosdok_id00005910-410.18453/rosdok_id00005910Besides some remarks on hit-and-miss hyperspaces and (relative) compactness of unions of (relative) compact sets, and using these together with a natural map from a function space between topological spaces into a function space between their Vietoris hyperspaces, we derive Ascoli-like theorems for some set-open topologies, nearly related to the compact-open, and mainly for the compact-open topology itself. Some Ascoli-like statements are given, where all requirements are focused on the set of functions, whose (relative) compactness is in question, not on the base spaces.20032003Preprints aus dem Institut für Mathematikrosdok_id000058161986139832Odvhttps://purl.uni-rostock.de/rosdok/id00005816Preprints aus dem Institut für Mathematik3255797-803/40003-0004https://purl.uni-rostock.de/rosdok/id000058163255797-8René Bartschepub.workingpaper1 Bartsch_nice_2003.pdf 222033 1fbc8e711fb3cd08b64962bff8ff9203 rosdok_id000059101987412443Oau2026-10-232026-10-23T08:48:05ZrdaConverted from PICA to MODS using Pica2MODS XSLT Transformer 2.14-SNAPSHOT [SCM: "" "" ""] with mode 'DEFAULT'.WorkingpaperOn a nice embedding and the Ascoli theoremBesides some remarks on hit-and-miss hyperspaces and (relative) compactness of unions of (relative) compact sets, and using these together with a natural map from a function space between topological spaces into a function space between their Vietoris hyperspaces, we derive Ascoli-like theorems for some set-open topologies, nearly related to the compact-open, and mainly for the compact-open topology itself. Some Ascoli-like statements are given, where all requirements are focused on the set of functions, whose (relative) compactness is in question, not on the base spaces.RenéBartsch1970 -VerfasserInaut1242054450009-0009-2471-2874https://purl.uni-rostock.de/rosdok/id00005910urn:nbn:de:gbv:28-rosdok_id00005910-410.18453/rosdok_id00005910510 MathematikMathematisch-Naturwissenschaftliche Fakultätalle Rechte vorbehaltenRechteinhaber Universität Rostockfrei zugänglich (Open Access)Lizenz Metadaten: CC0en1 Online-Ressource (19 Seiten)2003University of Rostock, Institute of MathematicsRostockmonographic20032026Universitätsbibliothek RostockRostock2026Universitätsbibliothek Rostockhttps://purl.uni-rostock.de/rosdok/id00005910René Bartschrosdok_id000058161986139832Odvhttps://purl.uni-rostock.de/rosdok/id00005816Preprints aus dem Institut für Mathematik3255797-803/40003-0004 2026-10-23T08:37:46.224Z 2026-10-23T08:48:09.301Z 2026-11-02T08:48:09.331Z editorKE {"identifier":"rosdok/id00005910","type":"local_id","additional":"","service":"MCRLocalID","created":"2026-10-23T08:37:46.260Z"} {"identifier":"urn:nbn:de:gbv:28-rosdok_id00005910-4","type":"dnbUrn","additional":"","service":"RosDokURN","created":"2026-10-23T08:37:46.277Z"} {"identifier":"https://purl.uni-rostock.de/rosdok/id00005910","type":"purl","additional":"","service":"RosDokPURL","created":"2026-10-23T08:37:46.282Z","registrationStarted":"2026-10-23T08:45:37.277Z"} {"identifier":"10.18453/rosdok_id00005910","type":"doi","additional":"","service":"RosDokDOI","created":"2026-10-23T08:37:46.288Z","registrationStarted":"2026-10-23T08:45:36.990Z","registered":"2026-10-23T08:45:38.382Z"} editorKEfulltextfile/rosdok_document_0000028047/rosdok_derivate_0000229951/Bartsch_nice_2003.pdfOn a nice embedding and the Ascoli theoremOn a nice embedding and the Ascoli theoremgnd:124205445orcid:0009-0009-2471-2874gnd:124205445orcid:0009-0009-2471-2874rosdok_document_0000028047-d3976421e49gnd:124205445orcid:0009-0009-2471-2874René BartschRené BartschRené BartschRené BartschRené BartschRostockUniversity of Rostock, Institute of Mathematicsepub.workingpaperhttps://purl.uni-rostock.de/rosdok/id00005910urn:nbn:de:gbv:28-rosdok_id00005910-410.18453/rosdok_id00005910Besides some remarks on hit-and-miss hyperspaces and (relative) compactness of unions of (relative) compact sets, and using these together with a natural map from a function space between topological spaces into a function space between their Vietoris hyperspaces, we derive Ascoli-like theorems for some set-open topologies, nearly related to the compact-open, and mainly for the compact-open topology itself. Some Ascoli-like statements are given, where all requirements are focused on the set of functions, whose (relative) compactness is in question, not on the base spaces.20032003Preprints aus dem Institut für Mathematikrosdok_id000058161986139832Odvhttps://purl.uni-rostock.de/rosdok/id00005816Preprints aus dem Institut für Mathematik3255797-803/40003-0004https://purl.uni-rostock.de/rosdok/id000058163255797-8René Bartsch[xslt]Saxonrosdok_id00005910https://purl.uni-rostock.de/rosdok/id00005910198741244310.18453/rosdok_id00005910urn:nbn:de:gbv:28-rosdok_id00005910-4René BartschBartsch RenéOn a nice embedding and the Ascoli theoremWorkingpaperworking paperUniversity of Rostock, Institute of Mathematics, 2003Besides some remarks on hit-and-miss hyperspaces and (relative) compactness of unions of (relative) compact sets, and using these together with a natural map from a function space between topological spaces into a function space between their Vietoris hyperspaces, we derive Ascoli-like theorems for…rosdok_id000058160003-000403/4René BartschOn a nice embedding and the Ascoli theoremPreprints aus dem Institut für MathematikUniversitätsbibliothek Rostockhttps://purl.uni-rostock.de/rosdok/id00005910RenéBartsch1970 -VerfasserInaut1242054450009-0009-2471-2874[purl]https://purl.uni-rostock.de/rosdok/id00005910[urn]urn:nbn:de:gbv:28-rosdok_id00005910-4[doi]10.18453/rosdok_id00005910open_access20032003epoch:21th_centuryrfc5646:endoctype:epub.workingpaperaccesscondition:openaccessSDNB:510institution:unirostock.mnfstate:published