Cyberworlds are being formed in cyberspaces as computational spaces. Now cyberspaces are rapidly expanding on the Web either intentionally or spontaneously, with or without design. Widespread and intensive local activities are melting each other on the web globally to create cyberworlds. The major key players of cyberworlds include e-finance that trades a GDP-equivalent a day and e-manufacturing that is transforming industrial production into Web shopping of product components and assembly factories. Lacking proper theory and design, cyberworlds have continued to grow chaotic and are now out of human understanding and control. This research first presents a generic theoretical framework and design based on algebraic topology, and also provides an axiomatic approach to theorize the potentials of cyberworlds.

Recent advances of Web information systems such as e-commerce and e-learning have created very large but hidden demands on conceptual multiresolution analysis for more generalized information analysis, cognition and modeling. To meet the demands in a general way, its modeling is formulated based on modern algebraic topology. To be specific, the modeling formulation is worked out in an incrementally modular abstraction hierarchy with emphasis on the two levels of the hierarchy appropriate for conceptual modeling: the adjunction space level and the cellular structured space level. Examples are shown to demonstrate the usefulness of the presented model as well as an implementation of a flower structure case.