Jonathon Funk and E.D. Tymchatyn, Unramified maps, JP Jour. Geom. Topol. 1:249--280, 2001.  Home/Search   Document Not in Database   Summary   Related Articles

....But then # # (X) # # 1 (X) # # 2 (X) is locally constant in E 1 E 2 by Lemma 5.2, and so X is locally constant in E by Lemma 5.4. # Our third example, which will be discussed in more detail in [10] involves the notion of unramified morphism, which in topos theory has been dealt with in [12, 21]. One can argue that this example historically preceded that of C (E ) E lc in the theory of Riemann surfaces [35] and that only on account of the desired connection with the fundamental group were additional assumptions made on the spaces, assumptions which in practice had the e#ect of ....

....C (E ) E lc in the theory of Riemann surfaces [35] and that only on account of the desired connection with the fundamental group were additional assumptions made on the spaces, assumptions which in practice had the e#ect of reducing the maps to just the covering projections. Explicitly, recall [12, 21] that an object A of a locally connected S topos E is called a complete spread object if the corresponding local homeomorphism E A E is a complete spread. Since such local homeomorphisms are precisely the unramified maps among the complete spreads, the full subcategory of E consisting of the ....

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Jonathon Funk and E.D. Tymchatyn, Unramified maps, JP Jour. Geom. Topol. 1:249--280, 2001.

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