The statement that F is a simple surface means: F is a function with initial set

Question

The statement that F is a simple surface means: F is a function with initial set a subset of the plane and final set a subset of the numbers. If (a, b) is in the initial set of F and the second number of an ordered pair in F, with first point (a, 6), is w. then this ordered pair is denoted by {(a, b), w). The number w is sometimes denoted by F((a, b)). Hence ((a, b), w) may be denoted by ((a, b), F((a, b))) or simply (a, b, F(a, b)). Note that (a, b, F(a, b)) is sometimes called an ordered number triple. Horizontal plane Definition 28. The statement that H is a horizontal plane means there is a number h and H is the simple surface with initial set the plane and final set only contains the number h. Simple surface property C Definition 29. The statement that the simple surface F has property C at the ordered pair ((a, b), F(a, b)), i.e., at the ordered number triple (a, b, F(a, b)), means: if H and K are two horizontal planes with F(a, b) between H(a, b) and K(a, b), then there is a plane segment PS containing (a, b) such that if (x, y) is a point in PS and in D_F, then F(x, y) is between H(a, b) and K(a, b). That is, the ordered number triple (a, b, F(a, b) is between H and H. PROBLEM 24. Suppose F is a simple surface with initial set the plane interval [I, J] and F has property C at every ordered number triple of F, then there is a horizontal plane H such that no ordered number triple of F is above H. Explain your answer using English sentences. PROBLEM 25. Suppose F is a simple surface with initial set the plane interval [I, J] and F has property C at every ordered number triple of F, then there is a horizontal plane H such that no ordered number triple of F is above H and there in a point of F that belongs to H. Explain your answer using English sentences.

Explanation / Answer

in this they are saying that F is an any surface which has interval [I,J] and F follows a special type of property that is C at every ordered number triple of F.Now there is a horizontal plane H and there is no orderd nuber triple of F is above H.

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