DOI: https://doi.org/10.14710/jfma.v0i0.27702

ON PROPERTIES OF PROJECTIVE SPACE DETERMINED BY QUOTIENT MAP

*Edi Kurniadi  -  Department of Mathematics of FMIPA of Universitas Padjadjaran, Indonesia
Badrulfalah Badrulfalah  -  Departemen Matematika FMIPA Unpad, Indonesia

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Abstract

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.

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Keywords: Projective space, Quotient map, Quotient topology, Subspaces, Smooth manifold

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Section: FUNDAMENTAL MATHEMATICS AND APPLICATIONS
Language : EN
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