V članku proučujemo različne variante periferne acikličnosti in lokalnih homotopskih lastnosti ter posplošimo in razširimo prejšnje rezultate R. C. Lacherja, D. R. McMillana in drugih avtorjev. Nato ...dobimo nekaj uporabnih rezultatov za celičaste dekompozicije mnogoterosti in konstruiramo eksotične faktorje (t.j. homološke mnogoterosti) za nekatere evklidske prostore.
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