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Test2Guide

# Test2Guide - Let D R D is said to be convex if a,b D the...

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Let ≠ D R. D is said to be convex if 2200 a,b D, the line segment connecting and is contained in D. Let ≠ D R. D is said to be connected if 2200 , D, 5 φ : [0,1] D such that φ (0) = , φ (1) = Let D ≠ . , x 0 D. f is continuous at x 0 if 2200 {a n } x 0 , a n D, {f(x n )} f(x 0 ). Let D ≠ . , x 0 D. f is continuous at x 0 if 2200ε > 0, such that if | x – x 0 | < δ , x D, |f(x) – f(x 0 )| < ε Let ≠ D R. . is said to be uniformly continuous on D if 2200 {u n }, {v n } D if {u n - v n } 0, then | (u n ) – (v n ) | 0 Let ≠ D R. . is said to be uniformly continuous on D if 2200ε > 0, such that if | x – y | < δ , x,y D, |f(x) – f(y)| < ε Let O R. O is said to be open if for any r O, > 0 such that (r- ε , r+ ε ) O Let D R. O i , i I, be open. If D , then is an open cover of D. Let ≠ D R. x 0 D. We say x 0 is an isolated point of D if >0 such that (x 0 - ε , x 0 + ε ) D = { x 0 } Let ≠ D R. . is said to be monotonically increasing if for u , v D, u ≤ v, (u) ≤ (v) Let ≠ D R. .

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