Author: José de Jesús García Ruvalcaba
Date: 15:11:54 11/22/99
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On November 22, 1999 at 14:29:27, Tord Romstad wrote: >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. > You are right on my interpretation of continuity. And yes, I meant the discrete topology for the space of all chess positions, it seems completely natural for me. José. >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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