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# weakly uniform cover ¤ÎÊÑ¹¹ÅÀ

 *Definition [#we2a5ac7]
A cover ¦Ë of a pseudo uniform space (X,U) is said to be weakly uniform if there exists a sequence ¦Á_n in U satisfying the following conditions:
+for any x in X, there exists an n in N and an L in ¦Ë such that ¦Á_n[x] is contained in L;
+$\{\alpha_{n+1}[\alpha_{n+1}[x]]:x\in X\}$ refines $\{\alpha_n[x]:x\in X\}$.
+&ref(http://www.eaflux.com/imgtex/imgtex.fcgi?%5bres=100%5d%7b$%5c%7b%5calpha_%7bn+1%7d%5b%5calpha_%7bn+1%7d%5bx%5d%5d:x%5cin%20X%5c%7d$%7d%25.png); refines &ref(http://www.eaflux.com/imgtex/imgtex.fcgi?%5bres=100%5d%7b$%5c%7b%5calpha_n%5bx%5d:x%5cin%20X%5c%7d$%7d%25.png);.
*Reference [#g7eb380a]
D. K. Musaev, ''Uniformly superparacompact, completely paracompact, and strongly paracompact uniform spaces'', J. Math. Sci., Vol.144, No.3, 2007