A Four Flagged Lemma
A Four Flagged Lemma
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In our eReader you can find the full English version of the book. Read A Four Flagged Lemma Online - link to read the book on full screen. Our eReader also allows you to upload and read Pdf, Txt, ePub and fb2 books. In the Mini eReder on the page below you can quickly view all pages of the book - Read Book A Four Flagged Lemma
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= ir (x) . Then any function f which makes the 1 X^ diagram -> v(X) commute is continuous, -3- Proof ; Let W be a subbaslc open set in E^. It suffices to show that f~^W is open. Assume, without loss of generality, that W = {w e E^ I w > w }. If w i u(X), then the connectedness of u(X) C E^ implies that either (i) w u(x) for all x e X. If (i) holds, then u"^(W) = X, so that v(u"nw)) = v(X) = f~^(W) is open. If (ii) holds, then u"^(W) = = v(u"^(W)) = f"^(W) is open. So, assume w* e u(X), * * * i.... E. , that w = u(x ) for some x e X. Then, as u preserves the complete preorder x }, which is open (showing u to be continuous) by the semiclosedness of v^(x ^)}, where x ^ = tt^ (x ), so that i v^(Pj, ) is again open. Thus v(u-^(W)) = H v^(P^) is open, and, M from the commutativity v u"^ = f"^, we conclude that f~'^(W) is open, as to be shown.
What to read after A Four Flagged Lemma?
You can find similar books in the "Read Also" column, or choose other free books by Murat R Sertel to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
= ir (x) . Then any function f which makes the 1 X^ diagram -> v(X) commute is continuous, -3- Proof ; Let W be a subbaslc open set in E^. It suffices to show that f~^W is open. Assume, without loss of generality, that W = {w e E^ I w > w }. If w i u(X), then the connectedness of u(X) C E^ implies that either (i) w u(x) for all x e X. If (i) holds, then u"^(W) = X, so that v(u"nw)) = v(X) = f~^(W) is open. If (ii) holds, then u"^(W) = = v(u"^(W)) = f"^(W) is open. So, assume w* e u(X), * * * i.... E. , that w = u(x ) for some x e X. Then, as u preserves the complete preorder x }, which is open (showing u to be continuous) by the semiclosedness of v^(x ^)}, where x ^ = tt^ (x ), so that i v^(Pj, ) is again open. Thus v(u-^(W)) = H v^(P^) is open, and, M from the commutativity v u"^ = f"^, we conclude that f~'^(W) is open, as to be shown.
What to read after A Four Flagged Lemma?
You can find similar books in the "Read Also" column, or choose other free books by Murat R Sertel to read onlineMoreLess
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