Author: Tord Romstad
Date: 11:29:27 11/22/99
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On November 20, 1999 at 14:22:14, Robert Hyatt wrote: >On November 20, 1999 at 12:31:11, José de Jesús García Ruvalcaba wrote: > >>Hi Bob, >> strictly speaking, the evaluation function is always continous, as its domain >>is a discrete space. Of course I understand what you mean, wanting a "more >>continous" evaluation function, i.e., one with less variation. >>José. > > >No it isn't... I think you and José use the word "continous" with different meanings. José means that evaluation functions are continuos in the topological sense, meaning that the inverse image of open sets are open. The truth of this statement depends on the topologies chosen on the domain and range of the evaluation function. I assume that José chooses the discrete topology (in which _all_ subsets are open) for the domain (i.e. the space of all possible chess positions). With this topology (there are many other possible topologies on the domain) any evaluation function is obviously continous. On the other hand, you seem to use the word "continous" in a more intuitive sense. To points (chess positions) in the domain are considered "close" if it is possible to reach one of the positions from the other one in a small number of good moves. Given two points which are close to each other in this sense, the evaluation function should return values which are also close. Tord
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