We present two propositions, each with a proof, and a theorem to establish a foundational framework for a novel perspective on quantum information framed in terms of differential geometry and topology. In particular, we show that the mapping to naturally encodes the binary outcomes of entangled quantum states, providing a minimal yet powerful abstraction of quantum duality. Building on this, we introduce the concept of a \emph{discrete fiber bundle} to represent quantum steering and correlations, where each fiber corresponds to the two possible measurement outcomes of entangled qubits. This construction offers a new topological viewpoint on quantum information, distinct from traditional Hilbert-space or metric-based approaches. The present work serves as a preliminary formulation of this framework, with further developments to follow.