According to recent work of Bounias and Bonaly (2000), there is a close relationship between the conceptualiza-tion of biological life and mathematical conceptualization such that both of them co-depend on each other when discussing preliminary conditions for properties of biosystems. More pre-cisely, such properties can be realized only, if the space of orbits of members of some topological space X by the set of functions governing the interactions of these members is com-pact and complete. This result has important consequences for the maximization of complementarity in habitat occupation as well as for the reciprocal contributions of sub(eco)systems with respect to their structural mutualism. In this present paper it will be shown what this more technical result means in philosophi-cal terms with a view to the biosemiotic consequences. As this approach fits naturally into the Kassel programme of investigat-ing the relationship between the cognitive perceiving of the world and its communicative modeling (Zimmermann 2004a, 2005b), it is found that topology as formal nucleus of spatial modeling is more than relevant for the understanding of repre-senting and co-creating the world as it is cognitively perceived and communicated in its design. Also, its implications may well serve the theoretical (top-down) foundation of biosemiotics itself.
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