{"id":1261,"date":"2018-03-15T13:32:56","date_gmt":"2018-03-15T12:32:56","guid":{"rendered":"https:\/\/www.pmfst.unist.hr\/znanost\/?p=1261"},"modified":"2018-03-20T12:08:47","modified_gmt":"2018-03-20T11:08:47","slug":"grupa-za-topologiju","status":"publish","type":"post","link":"https:\/\/www.pmfst.unist.hr\/odjel-za-matematiku\/grupa-za-topologiju\/","title":{"rendered":"Grupa za topologiju"},"content":{"rendered":"<div class=\"wpb-content-wrapper\">[vc_row][vc_column width=&#8221;2\/6&#8243;][mk_icon_box icon=&#8221;mk-moon-man&#8221; title=&#8221;red.prof.dr.sc. Nikola Kocei\u0107 Bilan&#8221; text_size=&#8221;20&#8243; style=&#8221;boxed&#8221; icon_color=&#8221;#1e73be&#8221; icon_circle_color=&#8221;&#8221; icon_circle_border_color=&#8221;#1e73be&#8221; title_color=&#8221;#1e73be&#8221;]<img loading=\"lazy\" decoding=\"async\" class=\"alignleft wp-image-1264 size-thumbnail\" src=\"https:\/\/www.pmfst.unist.hr\/znanost\/wp-content\/uploads\/sites\/29\/2018\/03\/nikola-koceic-bilan-150x150.jpg\" alt=\"\" width=\"150\" height=\"150\" \/><\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<ul>\n<li>tel: +38521619265<\/li>\n<li><span style=\"color: #3366ff;\"><strong>kabinet <a style=\"color: #3366ff;\" href=\"https:\/\/www.pmfst.unist.hr\/wp-content\/uploads\/2018\/03\/b3_14_17.jpg\">B3-15<\/a><\/strong><\/span><\/li>\n<li><a title=\"koceic@pmfst.hr\" href=\"mailto:koceic@pmfst.hr\">koceic@pmfst.hr<\/a><\/li>\n<\/ul>\n[\/mk_icon_box][\/vc_column][vc_column width=&#8221;2\/6&#8243;][mk_title_box color=&#8221;#1e73be&#8221; font_family=&#8221;none&#8221;]<strong>Odjel\/Katedra: <\/strong><\/p>\n<p>Odjel za matematiku[\/mk_title_box][mk_title_box color=&#8221;#1e73be&#8221; font_family=&#8221;none&#8221;]<b>\u010clanovi grupe<\/b>[\/mk_title_box][vc_column_text css=&#8221;.vc_custom_1520591816036{margin-bottom: 0px !important;}&#8221;]\n&#8211; prof.dr.sc. Vlasta Matijevi\u0107<br \/>\n&#8211; dr.sc. Goran Erceg<br \/>\n&#8211; Ivan Jeli\u0107. mag. math.<br \/>\n&#8211; dr.sc. Zdravko \u010cuka, FGAG, Split<br \/>\n&#8211; Ivan\u010dica Miro\u0161evi\u0107, FESB, Split<br \/>\n[\/vc_column_text][vc_column_text css=&#8221;.vc_custom_1520591712979{margin-bottom: 0px !important;}&#8221;]\n<h4>Podru\u010dje istra\u017eivanja:<\/h4>\n<p>&#8211; Op\u0107a topologija<br \/>\n&#8211; Algebarska topologija<br \/>\n&#8211; Teorija oblika i grubog oblika<br \/>\n&#8211; Teorija kontinuuma<br \/>\n&#8211; Generalizirani inverzni limesi<br \/>\n[\/vc_column_text][\/vc_column][vc_column width=&#8221;1\/6&#8243;][\/vc_column][\/vc_row][vc_row][vc_column width=&#8221;5\/6&#8243;][vc_separator color=&#8221;mulled_wine&#8221; style=&#8221;shadow&#8221; border_width=&#8221;3&#8243;][\/vc_column][vc_column width=&#8221;1\/6&#8243;][\/vc_column][\/vc_row][vc_row][vc_column width=&#8221;5\/6&#8243;][vc_column_text css=&#8221;.vc_custom_1520591748316{margin-bottom: 0px !important;}&#8221;]\n<h4>Opis istra\u017eivanja:<\/h4>\n<p>Polje istrazivanja je op\u0107a i algebarska topologija, posebno istra\u017eivanja u kojima se koriste tehnike aproksimacije topolo\u0161kih prostora limesima inverznih poliedarskih i ANR sistema.<br \/>\nDrugo podru\u010dje istra\u017eivanja je teorija oblika, posebno njezino poop\u0107enje teorija gruboga oblika. U zadnje vrijeme su otkrivene razli\u010dite i topolo\u0161ke i algebarske invarijante gruboga oblika s mogu\u0107im primjenama na op\u0107u topologiju i homotopsku teoriju. Tu se posebno isti\u010du grupe gruboga oblika i povezanost putovima gruboga oblika.<br \/>\nU sklopu istra\u017eivanja u teoriji kontinuuma definirana je kategorija CU u kojoj su objekti kompaktni metri\u010dki prostori, a morfizmi su odozgo poluneprekidne (u.s.c.) funkcije. Razmatraju se inverzni nizovi u kategoriji CU i dokazuje da s odgovaraju\u0107im morfizmima \u010dine kategoriju, ozna\u010denu s ICU. Rezultati su primjenjeni da se poka\u017ee, uz odre\u0111ene uvjete, homeomorfnost inverznih limesa inverznih nizova u kojima su objekti inverzni limesi. Nadalje, razmatra se poop\u0107enje pojma topolo\u0161ke entropije koji su uveli Adler, Konheim, and McAndrew na zatvorene podskupove od [0,1]2 koriste\u0107i Mahavierov produkt, objekt kojeg su definirale Greenwood i Kennedy. Pokazuje se da je nova definicije topolo\u0161ke entropije zaista dobra i koriste\u0107i entropiju tzv. funkcije pomaka (funkcija u uobi\u010dajenom smislu) pokazuje se da je uskla\u0111ena s prija\u0161njim definicijama entropije.<br \/>\n[\/vc_column_text][vc_column_text css=&#8221;.vc_custom_1520591959083{margin-bottom: 0px !important;}&#8221;]\n<h4><strong>Kontakti s akademskim i drugim institucijama:<\/strong><\/h4>\n<p>&#8211; University of Maribor, Slovenia<br \/>\n&#8211; Waseda University, Tokyo, Japan<br \/>\n&#8211; University of Skopje, Institute of Mathematics, Macedonia<br \/>\n&#8211; Warsaw University of Technology, Var\u0161ava, Poland<br \/>\n&#8211; University of Richmond, Richmond VA, USA<br \/>\n&#8211; Lamar University, Beaumont TX, USA<br \/>\n&#8211; University of Perugia, Department of Mathematics and computer science, Italy<br \/>\n[\/vc_column_text][\/vc_column][vc_column width=&#8221;1\/6&#8243;][\/vc_column][\/vc_row][vc_row][vc_column width=&#8221;5\/6&#8243;][vc_column_text css=&#8221;.vc_custom_1520591973324{margin-bottom: 0px !important;}&#8221;]\n<h4><strong>Opis dosada\u0161nje suradnje:<\/strong><\/h4>\n<p>V. Matijevi\u0107 je 2007. i 2011. boravila po 10 dana na Warsaw University of Technology, Var\u0161ava, Poljska, kao pozvani predava\u010d na topolo\u0161kom seminaru<br \/>\n&#8211; V. Matijevi\u0107 je 2009. boravila 5 dana na University of Maribor, Slovenia, kao pozvani predava\u010d na topolo\u0161kom seminaru<br \/>\n&#8211; N. Kocei\u0107 je 2010. boravio 5 dana na Sveu\u010dili\u0161te u Skopju, Institut za matematiku, Makedonija, kao pozvani predava\u010d na topolo\u0161kom seminaru<br \/>\n&#8211; G. Erceg je boravio 2010. i 2013. po 5 dana na University of Maribor, Slovenia<br \/>\nu sklopu zananstvene surandje<br \/>\n&#8211; V. Matijevi\u0107 je 2012. boravila 5 dana na Sveu\u010dili\u0161te u Skopju, Institut za matematiku, Makedonija, kao pozvani predava\u010d na topolo\u0161kom seminaru<br \/>\n&#8211; N. Kocei\u0107 i V. Matijevi\u0107 su ak. godine 2013.\/14. boravili 15 dana na Waseda University, Tokio, Japan, kao pozvani predava\u010di na dvije topolo\u0161ke konferencije<br \/>\n[\/vc_column_text][vc_column_text css=&#8221;.vc_custom_1521113815978{margin-bottom: 0px !important;}&#8221;]\n<h4><strong>Planovi budu\u0107ih istra\u017eivanja:<\/strong><\/h4>\n<p>U zadnje vrijeme prou\u010davani su prostori natkrivanja i nadlaganja nad (lokalno) kompaktnim topolo\u0161kim grupama. Ta ce se istra\u017eivanja nastaviti u smjeru daljnjeg ispitivanja svojstava prostora nadlaganja nad drugim klasama povezanih topolo\u0161kih grupa.<br \/>\nU podru\u010dju gruboga oblika planira se ispitati mogu\u0107nost topologiziranja grupa gruboga oblika tako da one postanu topolo\u0161ke grupe. Tako\u0111er, prou\u010dit \u0107e se mogu\u0107nosti druga\u010dijih pristupa (unutarnjih) grubome obliku od pristupa preko inverznih sustava. Napokon, ispitati \u0107e se mogu\u0107e primjena teorije gruboga oblikana dinami\u010dke sisteme.<br \/>\nU sklopu istra\u017eivanja u teoriji kontinuuma daljnji plan je pro\u0161irenje nove definicije topolo\u0161ke entropije na \u0161iru klasu prostora (kompaktne metri\u010dke prostore), eventualno odre\u0111ivanje uvjeta za trivijalnu topolo\u0161ku entropiju i daljnja primjena dobivenog u teoriji o generaliziranim inverznim limesima i op\u0107enitije u teoriji kontinuuma i topolo\u0161kih dinami\u010dkih sistema. Nadalje, cilj je generalizirane inverzne limes koje su uveli Ingram i Mahavier opisati u nekoj novoj kategoriji tako da budu inverzni limesi u kategorolo\u0161kom smislu. U dosad definiranim kategorijama oni to nisu. [\/vc_column_text][\/vc_column][vc_column width=&#8221;1\/6&#8243;][\/vc_column][\/vc_row][vc_row][vc_column width=&#8221;5\/6&#8243;][vc_column_text css=&#8221;.vc_custom_1520603890149{margin-bottom: 0px !important;}&#8221;]\n<h4>Popis odabranih znanstvenih radova:<\/h4>\n<p>&#8211; K. Eda, J. Mandi\u0107 and V. Matijevi\u0107, Torus-like continua which are not self-covering spaces, Topology Appl. 153 (2005), 359-369.<br \/>\n&#8211; K. Eda and V. Matijevi\u0107, Finite-sheeted covering maps over 2-dimensional connected, compact abelian groups, Topology Appl. 153 (2006), 1033&#8211;1045.<br \/>\n&#8211; V. Matijevi\u0107, Finite-sheeted covering maps over Klein bottle weak solenoidal spaces, Glasnik Mat. 42 (62) (2007), 19-41.<br \/>\n&#8211; K. Eda and V. Matijevi\u0107, Finite-index supergroups and subgroups of torsionfree abelian groups of rank two, Journal Alg.319 (2008), 3567-3587.<br \/>\n&#8211; L.J. Hernandez Paricio and V. Matijevi\u0107, Fundamental groups and finite sheeted coverings, Journal Pure Appl. Alg. 214 (2009), 281-296.<br \/>\n&#8211; N. Ugle\u0161i\u0107 and V. Matijevi\u0107, On expansions and pro-pro-categories, Glasnik Mat.45 (2010), 173-217.<br \/>\n&#8211; V. Matijevi\u0107, A note on finite-sheeted covering maps from 2-dimensional compact abelian groups, Topology Appl. 153 (2010) 2746-2756.<br \/>\n&#8211; K. Eda and V. Matijevi\u0107, Covering maps over solenoids which are not covering homomorphisms, Funadmenta Math. 221 (2013).<br \/>\n&#8211; K. Eda and V. Matijevi\u0107, Existence and uniqueness of topological group structures on covering spaces over groups, Fundamenta Math. (to appear) submitted.<br \/>\n&#8211; N. Kocei\u0107 Bilan, N. Ugle\u0161i\u0107, The coarse shape, Glasnik Matemati\u010dki 42 (62) (2007), 145-187.<br \/>\n&#8211; A. Kadlof, N. Kocei\u0107 Bilan, N. Ugle\u0161i\u0107, Borsuk.s quasi equivalence is not transitive, Fundamenta Mathematicae 197 (2007), 215-227.<br \/>\n&#8211; N. Kocei\u0107 Bilan, The coarse shape groups, Topology and its Application 157 (2010), 894-901.<br \/>\n&#8211; N. Kocei\u0107 Bilan, On some coarse shape invariants, Topology and its Appl. 157 (2010) 2679-2685.<br \/>\n&#8211; N. Kocei\u0107 Bilan, N. Ugle\u0161i\u0107, The coarse shape path connectedness, Glasnik Mat. 46 (66) (2011), 489-503<br \/>\n&#8211; N. Kocei\u0107 Bilan, Towards the algebraic characterization of (coarse) shape path connectedness, Topology and its Applications 160 (2013) 538-545<br \/>\n&#8211; N. Kocei\u0107 Bilan, Computing coarse shape groups of solenoids, Mathematical communications 14 (2014), 243-251<br \/>\n&#8211; N. Kocei\u0107 Bilan, I. Jeli\u0107, On intersections of the exponential and logarithmic curves, Annales Mathematicae et Informaticae 43 (2014) 159-170<br \/>\n&#8211; N. Kocei\u0107 Bilan, Continuity of coarse shape groups, Homology, Homotopy and Applications, vol.18(2), (2016), 209-215<br \/>\n&#8211; I. Bani\u010d, M. \u010crepnjak, G. Erceg, M. Merhar and U. Milutinovi\u0107, Inducing functions between inverse limits with upper semicontinuous bonding functions, Houston J. Math. Vol. 41, No. 3 (2015), 1021-1037<\/p>\n[\/vc_column_text][\/vc_column][vc_column width=&#8221;1\/6&#8243;][\/vc_column][\/vc_row]\n<\/div>","protected":false},"excerpt":{"rendered":"<p>[vc_row][vc_column width=&#8221;2\/6&#8243;][mk_icon_box icon=&#8221;mk-moon-man&#8221; title=&#8221;red.prof.dr.sc. Nikola Kocei\u0107 Bilan&#8221; text_size=&#8221;20&#8243; style=&#8221;boxed&#8221; icon_color=&#8221;#1e73be&#8221; icon_circle_color=&#8221;&#8221; icon_circle_border_color=&#8221;#1e73be&#8221; title_color=&#8221;#1e73be&#8221;] &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; tel: +38521619265 kabinet B3-15 koceic@pmfst.hr [\/mk_icon_box][\/vc_column][vc_column width=&#8221;2\/6&#8243;][mk_title_box color=&#8221;#1e73be&#8221; font_family=&#8221;none&#8221;]Odjel\/Katedra: Odjel za matematiku[\/mk_title_box][mk_title_box color=&#8221;#1e73be&#8221; font_family=&#8221;none&#8221;]\u010clanovi grupe[\/mk_title_box][vc_column_text css=&#8221;.vc_custom_1520591816036{margin-bottom: 0px !important;}&#8221;] &#8211; prof.dr.sc. Vlasta Matijevi\u0107 &#8211; dr.sc. Goran Erceg &#8211; Ivan Jeli\u0107. mag. math. &#8211; dr.sc. [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":1388,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"rs_blank_template":"","rs_page_bg_color":"","slide_template_v7":"","footnotes":""},"categories":[3],"tags":[],"class_list":["post-1261","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-odjel-za-matematiku-istrazivacka-grupa"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.4 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Grupa za topologiju - Odjel za matematiku<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.pmfst.unist.hr\/odjel-za-matematiku\/grupa-za-topologiju\/\" \/>\n<meta property=\"og:locale\" content=\"hr_HR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Grupa za topologiju - Odjel za matematiku\" \/>\n<meta property=\"og:description\" content=\"[vc_row][vc_column width=&#8221;2\/6&#8243;][mk_icon_box icon=&#8221;mk-moon-man&#8221; title=&#8221;red.prof.dr.sc. 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