By Bernhard Möller, John V. Tucker

Preface VI I X desk of Contents B. Möller and J.V. Tucker (Eds.): clients for Foundations, LNCS 1546, pp. 1-26, 1998. Springer-Verlag Berlin Heidelberg 1998 2 The NADA crew creation: NADA and 0 three four The NADA crew creation: NADA and zero five 6 The NADA workforce advent: NADA and zero 7 eight The NADA workforce advent: NADA and 0 nine 10 The NADA crew creation: NADA and 0 eleven 12 The NADA staff advent: NADA and zero thirteen 14 The NADA staff advent: NADA and zero 15 sixteen The NADA workforce advent: NADA and zero 17 18 The NADA team creation: NADA and 0 19 20 The NADA staff creation: NADA and zero 21 22 The NADA crew advent: NADA and 0 23 24 The NADA team advent: NADA and 0 25 26 The NADA staff Streams, flow Transformers and area Representations B. Möller and J.V. Tucker (Eds.): customers for Foundations, LNCS 1546, pp. 27-68, 1998. Springer-Verlag Berlin Heidelberg 1998 28 J. Blanck, V. Stoltenberg-Hansen, and J.V. Tucker Streams, move Transformers and area Representations 29 30 J. Blanck, V. Stoltenberg-Hansen, and J.V. Tucker Streams, move Transformers and area Representations 31 32 J. Blanck, V. Stoltenberg-Hansen, and J.V. Tucker Streams, circulation Transformers and area Representations 33 34 J. Blanck, V. Stoltenberg-Hansen, and J.V. Tucker Streams, circulation Transformers and area Representations 35 36 J. Blanck, V. Stoltenberg-Hansen, and J.V. Tucker Streams, circulate Transformers and area Representations 37

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The next step is to represent continuous functions between topological spaces. 3. Let D; DR ;  and E; E R;  be domain representations of X and Y respectively. A function f: X ! Y is represented by or lifts to a  R  E R and fx  = fx, for all continuous function f: D ! E if fD R x2D . 48 J. Blanck, V. V. Tucker This means that the following diagram commutes. f D E fj R DR D E R   f X Y Let D; DR ;  and E; E R ;  be domain representations of X and Y respectively. Suppose f: D !

We refer to 47 for a discussion of approximation structures. The next step is to represent continuous functions between topological spaces. 3. Let D; DR ;  and E; E R;  be domain representations of X and Y respectively. A function f: X ! Y is represented by or lifts to a  R  E R and fx  = fx, for all continuous function f: D ! E if fD R x2D . 48 J. Blanck, V. V. Tucker This means that the following diagram commutes. f D E fj R DR D E R   f X Y Let D; DR ;  and E; E R ;  be domain representations of X and Y respectively.

B  T ! Rn  B n ! A ! T ! A; be de ned by n '; 1; : : :; n; t = ' 1 t; : : :; ' n t: ii A stream transformer F: R ! B ! T ! 5. 6 can now be expressed as G' = 2'; 1 ; 2; ; where 1, 2 and  are the transformations extracted in the example. Accessing an interval of the input stream. 8. Let G: R ! R ! R ! R be de ned by Gft = xmax fx: 2 0;t 36 J. Blanck, V. V. Tucker The stream transformer G depends on a continuum of values of the input stream so there is no possibility of modifying the single access model in the way done above for a nite number of accesses to the input stream.

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