ON PROPERTIES OF PROJECTIVE SPACE DETERMINED BY QUOTIENT MAP

Kurniadi, Edi
Badrulfalah, Badrulfalah

Journal of Fundamental Mathematics and Applications (JFMA)
Vol 8, No 2 (2025)

The state of a system in quantum theory is not always described by an element of a Hilbert space but by an element of projective space. The research aims to prove that the real projective space consisting of one-dimensional linear subspaces is a smooth manifold which is constructed by a quotient map. It is shown that a projective space is a Hausdorff space, second countable, and -dimensional locally Euclidean. It is also proved that the -dimensional real a projective space is homeomorphic to the quotient topology . The proof involves a quotient map which is defined by a quotient topology.