By Jane Nelsen, Lynn Lott, H. Stephen Glenn
The Acclaimed Bestseller which could enhance Your lecture room adventure Forever!
Over the years, thousands of oldsters have come to belief the vintage Positive Discipline sequence for its constant, commmonsense method of baby rearing. countless numbers of colleges additionally use those amazingly powerful recommendations for restoring order and civility to today's turbulent study rooms. Now it's also possible to use this philosophy as a origin for fostering cooperation, problem-solving abilities, and mutual appreciate in little ones. think, rather than controlling habit, you'll be educating; rather than confronting apathy, you'll get pleasure from prompted, keen scholars! within, you'll notice how you can:
·Create a lecture room weather that boosts educational studying
·Use encouragement instead of compliment and rewards
·Instill important social talents and confident habit by using classification conferences
·Understand the incentive in the back of students' habit rather than searching for factors
·And even more!
Over 1 million Positive Discipline books bought!
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Additional resources for Positive Discipline in the Classroom: Developing Mutual Respect, Cooperation, and Responsibility in Your Classroom (3rd Edition)
Proof. (i) (ii) If yo If Xo E Yo and x0 E Xo with n(xo) = yo, then is a minimal subset of X, then n(X) 3 n(Xo) (t E T). = Y, by (i). (iii) If n(xo) = $(xo), then n(x,t) and # agree on a dense set, so = #(xot) Thus n n = 14,. (iv) follows from (1) and the fact that the minimal subsets of a flow are disjoint or equal. Since our main interest is in minimal flows, it will usually not be necessary to specify that a homomorphism is onto. The meaning of the terms isomorphism, endomorphism, and automorphism should be clear.
Theorem. Let U n:X+Y be a homomorphism of minimal flows, and let be a non-empty open set in X. Then n(U) Proof. Let V has non-empty interior. be a closed set in X with V c U and int V f $. n Since X is minimal, there are t 1' . . ,tn E T such that Vti = X, so i=1 n n Y = n(X) = n(Vti) = n(V)ti. Therefore n(V)ti has non-empty intei=1 i=1 rior for some ti, so int n(V1 * 4. Since n(U) D n(V1, int n(U) * 4. u u u FIows and Minimal Sets Note that if s : X+Y is an onto homomorphism, then R(n) = R = [(x,~') 6 X x X)n(x) = n(x')l equivalence relation.
Thus G is a compact topological group and G acts as a group of homeomorphisms on X. Summarizing, we have proved: 2. Theorem. Let (X,T) be an equicontinuous flow. Then there is a compact group G and an action of G on X which extends the action of T. As we observed in the preceding chapter, if a compact group G on X, the action of C acts is equicontinuous, as is the action of any subgroup T of G. The theorem just proved shows that all equicontinuous flows arise this way. (X,T) is equicontinuous, its enveloping Next, we show that when semigroup coincides with G.
Positive Discipline in the Classroom: Developing Mutual Respect, Cooperation, and Responsibility in Your Classroom (3rd Edition) by Jane Nelsen, Lynn Lott, H. Stephen Glenn