Informalogical Space: Decomposition, Compactness and Isomorphism
نویسنده
چکیده
In a previous paper, we presented a meaning based information theory in which the core concept is an informalogical space. We introduced the concepts of an information net in an informalogical space, a piece of limit information of an information net, a separated informalogical space and a first countable informalogical space. We built a convergence theory of information nets and applied the convergence theory to information sequences. In this paper, we will introduce the concepts of decompositions of information and informalogical spaces, and we will prove some theorems about decompositions. We will introduce the concept of a compact informalogical space and prove that an informalogical space is compact if and only if each information net in the informalogical space has a subnet that converges. We will introduce the concept of an isomorphism between two informalogical spaces and the concept of an isomorphic invariant which is a property of informalogical spaces that is preserved under isomorphisms. We will prove that separatedness, limit uniqueness, first countability, and compactness are all isomorphic invariants.
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