Extreme diversities, versatility and dynamism of cloud computing applications with its high availability through smart devices such as smart phones and media are shown to be supported by the cyber world modeling in an incrementally modular abstraction hierarchy (IMAH) with homotopy extension property (HEP) and homotopy lifting property (HLP), as a transparent and highly universal modeling of smart cloud computing businesses to overcome combinatorial explosion of smart computing. It works to realize cost effective and visible businesses with high social impacts, both globally and locally, contributing to clarify smart cloud computing in the smart cloud imagery business.
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