November 14, 2025Open Access

The Topological Foundation of Information Theory

Key Points

The theory establishes information principles in spaces with an uncountable basis, expanding classical concepts.
Previous findings in countable basis spaces remain valid under this new framework of information theory.
The work introduces Type II as an extension that encompasses Type I, enabling new insights into information representation.
Extending to uncountable spaces may allow applications that were previously inaccessible with Type I methods.

Abstract

Classical information theory has been conducted exclusively in spaces with a countablebasis, Type I. We establish a theory of information in a space with an uncountable basis,Type II. Type I is one coordinate of Type II and in the unified space, Type I ⊂ Type II.All previous work in Type I remains valid. The expansion of the space to include Type IIopens new domains where Type I methods cannot be formulated.

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Cite This Study

Taylor, John, (Fri,) studied this question.

synapsesocial.com/papers/692519b4c0ce034ddc354486 https://doi.org/https://doi.org/10.5281/zenodo.17613137

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