Current Problems in Mathematical Analysis

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Across
  1. 1. d(x, y) = |x − y|, x, y ∈ X is known as ____ metric for such a set X
  2. 4. If f −1 is to be function, then each element y ∈ Y must correspond to some x ∈ X. Functions with this property are called ……….. .
  3. 5. . ………. of function, if for all x ∈ M
  4. 7. If the function y=f(x) is ____ on (a,b), then by definition, we can write: ∀x∈(a,b):x>x0⇒f(x)>f(x0)
  5. 8. The set X is called the ....... of the function f: X  Y
  6. 9. The ……….. of a set X , denoted by ~X , is the set of elements that do not belong to X; that is, ~X = { x : x ∉ X}
  7. 12. Function f(x) defined on the set D(f ) is called ______ iff there exists a real number K such, that for all x from D(f )holds:|f(x)|< K( f(x)≤K,f(x)≥K)
  8. 13. What is name of this rule? X ∩(Y ∩Z)=(X ∩Y) ∩Z
  9. 16. f : M → R, x → y = f (x)
  10. 17. WHICH SETS ARE EQUAL?
  11. 18. h(x)=f(x)× g(x)
  12. 19. Functions f(x) and g(x) are equal if and only if they are defined on the .... set of real numbers
Down
  1. 2. ...... value of a function is function h(x) defined on M and such, that for all x M holdsf :M R, xy f (x): , ( ) 0 h M Rxh x h(x) f (x)
  2. 3. A function that is both injective and surjective is called
  3. 6. Function h(x) = (f • g )(x) is called a …….. function
  4. 10. x ϵ M is ______ variable - argument of a function.
  5. 11. R+ is the set of all ______ numbers
  6. 14. d(x, z) d(x, y) + d(y, z) for all x, y, z ∈ X is known as______ inequality
  7. 15. Function f(x) is said to be ____ on M, if ꓯx: f(-x) = f(x)