{"?xml":{"@version":"1.0"},"edm:RDF":{"@xmlns:dc":"http://purl.org/dc/elements/1.1/","@xmlns:edm":"http://www.europeana.eu/schemas/edm/","@xmlns:wgs84_pos":"http://www.w3.org/2003/01/geo/wgs84_pos","@xmlns:foaf":"http://xmlns.com/foaf/0.1/","@xmlns:rdaGr2":"http://rdvocab.info/ElementsGr2","@xmlns:oai":"http://www.openarchives.org/OAI/2.0/","@xmlns:owl":"http://www.w3.org/2002/07/owl#","@xmlns:rdf":"http://www.w3.org/1999/02/22-rdf-syntax-ns#","@xmlns:ore":"http://www.openarchives.org/ore/terms/","@xmlns:skos":"http://www.w3.org/2004/02/skos/core#","@xmlns:dcterms":"http://purl.org/dc/terms/","edm:WebResource":[{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-DOJVS28A/cb4dfa66-0fa2-401e-b492-eb51656b45b5/PDF","dcterms:extent":"1146 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-DOJVS28A/40456ebd-50e0-4b71-add6-2460e13764a3/TEXT","dcterms:extent":"73 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-DOJVS28A/9929e33f-d962-42c4-b541-b6b1618efb90/PDF","dcterms:extent":"96 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-DOJVS28A/35cb35c5-dcb2-4465-b920-af02fd643050/TEXT","dcterms:extent":"4 KB"}],"edm:ProvidedCHO":{"@rdf:about":"URN:NBN:SI:doc-DOJVS28A","dcterms:issued":"2026","dc:creator":["Catalano, Domenico A.","D'Azevedo, Antonio Breda"],"dc:format":[{"@xml:lang":"sl","#text":"letnik:26"},{"@xml:lang":"sl","#text":"številka:3, article  p3.08"},{"@xml:lang":"sl","#text":"str. 1-28"}],"dc:identifier":["DOI:10.26493/1855-3974.3550.24e","ISSN:1855-3974","COBISSID_HOST:289928195","URN:URN:NBN:SI:doc-DOJVS28A"],"dc:language":"en","dc:publisher":{"@xml:lang":"sl","#text":"Univerza na Primorskem"},"dc:source":{"@xml:lang":"sl","#text":"Ars mathematica contemporanea"},"dc:subject":[{"@xml:lang":"sl","#text":"biorientabilni zemljevidi"},{"@xml:lang":"en","#text":"bi-orientable maps"},{"@xml:lang":"en","#text":"chiral"},{"@xml:lang":"sl","#text":"kiralni zemljevidi"},{"@xml:lang":"sl","#text":"orientabilni zemljevidi"},{"@xml:lang":"en","#text":"orientable maps"},{"@xml:lang":"sl","#text":"popolnoma kiralni zemljevidi"},{"@xml:lang":"en","#text":"pseudo Hurwitz"},{"@xml:lang":"sl","#text":"psevdo-Hurwitzevi zemljevid"},{"@xml:lang":"en","#text":"totally chiral"}],"dc:title":{"@xml:lang":"sl","#text":"Orientability versus bi-orientability|"},"dc:description":[{"@xml:lang":"sl","#text":"Topological orientability was first defined by Listing in 1861 followed closely by Möbius (1865); Möbius defined orientation by the existence of a coherent edges orientation of a net (polygonal) decomposition of a compact surface. After Euler's classification of compact surfaces, it was clear that the Möbious combinatorial definition only dependents on the surface and not on the particular polygonal decomposition. This makes orientability both a topological and a combinatorial property. A surface can be orientable or not, and so a given surface can support an orientable or a non-orientable map, but not both. In contrast, bi-orientable and non-bi-orientable maps (introduced by Steve Wilson in the seventies as pseudo-orientable maps) can both be present in the same surface. This makes bi-orientability a purely combinatorial property, nonetheless, it shows remarkable resemblances with orientability. These two categories of maps are connected by the Petrie dual operation. The present paper pretends to emphasise their similarities and their differences, having as main focus bi-orientable maps. In the present paper, maps are considered to have no semi-edges and no boundary"},{"@xml:lang":"sl","#text":"Topološko orientabilnost je prvi opredelil Listing leta 1861, kmalu zatem pa še Möbius (1865). Möbius je orientacijo definiral z obstojem skladne orientacije robov mrežne (poligonske) razčlenitve kompaktne ploskve. Po Eulerjevi klasifikaciji kompaktnih ploskev je jasno, da je Möbiusova kombinatorna definicija odvisna le od ploskve same in ne od konkretne izbire poligonske razčlenitve. Zaradi tega je orientabilnost hkrati topološka in kombinatorična lastnost. Ploskev je lahko orientabilna ali neorientabilna, zato lahko dana ploskev nosi bodisi orientabilen bodisi neorientabilen zemljevid, ne pa obeh hkrati. Nasprotno pa lahko na isti ploskvi obstajajo tako biorientabilni kot nebiorientabilni zemljevidi (ki jih je v sedemdesetih letih prejšnjega stoletja Steve Wilson uvedel pod imenom psevdoorientabilni zemljevidi). Zaradi tega je biorientabilnost povsem kombinatorična lastnost; kljub temu pa kaže presenetljive podobnosti z orientabilnostjo. Ti dve kategoriji zemljevidov sta povezani z operacijo Petrijevega duala. Namen tega članka je poudariti podobnosti in razlike med njima, pri čemer je glavni poudarek na biorientabilnih zemljevidih. V tem članku obravnavamo zemljevide brez pol-robov in brez roba ploskve"}],"edm:type":"TEXT","dc:type":[{"@xml:lang":"sl","#text":"znanstveno časopisje"},{"@xml:lang":"en","#text":"journals"},{"@rdf:resource":"http://www.wikidata.org/entity/Q361785"}]},"ore:Aggregation":{"@rdf:about":"http://www.dlib.si/?URN=URN:NBN:SI:doc-DOJVS28A","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-DOJVS28A"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-DOJVS28A/cb4dfa66-0fa2-401e-b492-eb51656b45b5/PDF"},"edm:rights":{"@rdf:resource":"http://creativecommons.org/licenses/by/4.0/"},"edm:provider":"Slovenian National E-content Aggregator","edm:intermediateProvider":{"@xml:lang":"en","#text":"National and University Library of Slovenia"},"edm:dataProvider":{"@xml:lang":"sl","#text":"Univerza na Primorskem, Fakulteta za naravoslovje, matematiko in informacijske tehnologije"},"edm:object":{"@rdf:resource":"http://www.dlib.si/streamdb/URN:NBN:SI:doc-DOJVS28A/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-DOJVS28A"}}}}