On semı-mınımal weakly open and semı
... In the year 2001 and 2003, F.Nakaoka and N.oda, [1-3] introduced and studied minimal open [resp. minimal closed ] sets which are subclass of open [resp.closed sets]. The family of all minimal open [minimal closed] in a topological space X is denoted by mio(X) [mic(X)]. Similarly the family of all ma ...
... In the year 2001 and 2003, F.Nakaoka and N.oda, [1-3] introduced and studied minimal open [resp. minimal closed ] sets which are subclass of open [resp.closed sets]. The family of all minimal open [minimal closed] in a topological space X is denoted by mio(X) [mic(X)]. Similarly the family of all ma ...
Five Lectures on Dynamical Systems
... If B) occurs, as the sequence Gn (0) ∈ [0, 1] is monotone, the limit z′ = limn→+∞ Gn (0) is a fixed point of G. This fixed point projects to a fixed point for f q . These contradictions prove that item i) may not occur. The same contradiction may be obtained in case ii) along the above lines. Detail ...
... If B) occurs, as the sequence Gn (0) ∈ [0, 1] is monotone, the limit z′ = limn→+∞ Gn (0) is a fixed point of G. This fixed point projects to a fixed point for f q . These contradictions prove that item i) may not occur. The same contradiction may be obtained in case ii) along the above lines. Detail ...
A NOTE ON Θ-CLOSED SETS AND INVERSE LIMITS
... Θ-closed (Theorem 2.13). We have the following consequence of Theorem 3.5. Corollary 3.6. Let X = {Xa , pab , A} be an inverse system of non-empty nearly-compact spaces. Then lim X is non-empty. Moreover, if pab are surjections, then the projections pa : lim X →Xa , a ∈ A, are surjections. Lemma 3.7 ...
... Θ-closed (Theorem 2.13). We have the following consequence of Theorem 3.5. Corollary 3.6. Let X = {Xa , pab , A} be an inverse system of non-empty nearly-compact spaces. Then lim X is non-empty. Moreover, if pab are surjections, then the projections pa : lim X →Xa , a ∈ A, are surjections. Lemma 3.7 ...
Transreal calculus - CentAUR
... until the axioms [6] or algorithms [3] of transreal arithmetic have been properly learned. The reader is further cautioned that the relational operators of transreal arithmetic, less-than (<), equal-to (=), greater-than (>), together with their negations, form a total, irredundant set of independen ...
... until the axioms [6] or algorithms [3] of transreal arithmetic have been properly learned. The reader is further cautioned that the relational operators of transreal arithmetic, less-than (<), equal-to (=), greater-than (>), together with their negations, form a total, irredundant set of independen ...
local contractibility, cell-like maps, and dimension
... if every continuous function from A' to a polyhedron is null homotopic. In addition, a continuous surjection /: X -» Y between compact spaces is called cell-like provided that f~l(y) has trivial shape for every y e Y. One of the most outstanding open problems in geometric topology is whether a cell- ...
... if every continuous function from A' to a polyhedron is null homotopic. In addition, a continuous surjection /: X -» Y between compact spaces is called cell-like provided that f~l(y) has trivial shape for every y e Y. One of the most outstanding open problems in geometric topology is whether a cell- ...
EXISTENCE AND PROPERTIES OF GEOMETRIC QUOTIENTS
... resp. the morphisms q and j/Y are surjective). If, in addition, q and j/Y are locally of finite type or integral, then these two conditions are equivalent to: (iii) For any algebraically closed field K, the map q(K) : X(K)/R(K) → Y (K) is surjective (resp. injective, resp. bijective). Proof. That (i ...
... resp. the morphisms q and j/Y are surjective). If, in addition, q and j/Y are locally of finite type or integral, then these two conditions are equivalent to: (iii) For any algebraically closed field K, the map q(K) : X(K)/R(K) → Y (K) is surjective (resp. injective, resp. bijective). Proof. That (i ...
Generalized rough topological spaces
... exactly one and only one element from each equvalance class of X. Then A = ( φ , X) is rough open. Thus the result 2.14 in general topological space is not valid in indiscrete rough topological space. Example 3.9. Consider X= ( X L , X U ) . Let A and B be any two proper exact subsets of XL and XU r ...
... exactly one and only one element from each equvalance class of X. Then A = ( φ , X) is rough open. Thus the result 2.14 in general topological space is not valid in indiscrete rough topological space. Example 3.9. Consider X= ( X L , X U ) . Let A and B be any two proper exact subsets of XL and XU r ...
