A generalization of the Levin-Rubin-Schapiro Factorization Theorem
Virk, Žiga, 1982-
Pri dani preslikavi ▫$f\colon X \to Y$▫ kompaktnih Hausdorffovih prostorov nam Mardešićev faktorizacijski izrek zagotavlja obstoj faktorizacije ▫$f = qj, j \colon X \to Z, q\colon Z \to Y$▫ skozi ...kompakten Hausdorffov prostor ▫$Z$▫ s lastnostjo ▫$\dim Z \leq \dim X$▫, pri čemer je teža ▫$Z$▫ navzgor omejena s težo ▫$Y$▫. Izrek je bil v preteklosti posplošen v okviru različnih kontekstov, pri čemer je bil Levin-Rubin-Schapirov faktorizacijski izrek eden izmed bolj opaznih rezultatov. Ta članek predstavi novo posplošitev, pri kateri faktorizacijski prostor ▫$Z$▫ podeduje razširitvene lastnosti vsake preslikave v smislu Levin-Rubin-Schapirovega faktorizacijskega izreka. Omenjena dednost se izraža z novim pojmom ekstenzionalne ekvivalence. Poleg tega obravnavamo vpliv take posplošitve na ekstenzionalno relacijo med preslikavami, ▫$f \tau i$▫.
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