ON PROPERTIES OF PROJECTIVE SPACE DETERMINED BY QUOTIENT MAP

Edi Kurniadi (Department of Mathematics of FMIPA of Universitas Padjadjaran)
Badrulfalah Badrulfalah (Departemen Matematika FMIPA Unpad)

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.