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In mathematics, real projective space, denoted or (), is the topological space of lines passing through the origin 0 in the real space +. It is a compact , smooth manifold of dimension n , and is a special case G r ( 1 , R n + 1 ) {\displaystyle \mathbf {Gr} (1,\mathbb {R} ^{n+1})} of a Grassmannian space.
Psychological projection is a defence mechanism of alterity concerning "inside" content mistaken to be coming from the "outside" Other. [1] It forms the basis of empathy by the projection of personal experiences to understand someone else's subjective world. [1]
External or sensory perception (exteroception), tells us about the world outside our bodies. Using our senses of sight, hearing, touch, smell, and taste, we perceive colors, sounds, textures, etc. of the world at large. There is a growing body of knowledge of the mechanics of sensory processes in cognitive psychology.
One common model of the real projective plane is the space of lines in three-dimensional Euclidean space which pass through a particular origin point; in this model, lines through the origin are considered to be the "points" of the projective plane, and planes through the origin are considered to be the "lines" in the projective plane.
v. t. e. Philosophy of psychology is concerned with the history and foundations of psychology. It deals with both epistemological and ontological issues and shares interests with other fields, including philosophy of mind and theoretical psychology. Philosophical and theoretical psychology are intimately tied and are therefore sometimes used ...
A projective space is a topological space, as endowed with the quotient topology of the topology of a finite dimensional real vector space. Let S be the unit sphere in a normed vector space V , and consider the function π : S → P ( V ) {\displaystyle \pi :S\to \mathbf {P} (V)} that maps a point of S to the vector line passing through it.
A mental representation (or cognitive representation), in philosophy of mind, cognitive psychology, neuroscience, and cognitive science, is a hypothetical internal cognitive symbol that represents external reality or its abstractions. [1][2] Mental representation is the mental imagery of things that are not actually present to the senses. [3]
For example, the group of projective geometry in n real-valued dimensions is the symmetry group of n-dimensional real projective space (the general linear group of degree n + 1, quotiented by scalar matrices). The affine group will be the subgroup respecting (mapping to itself, not fixing pointwise) the chosen hyperplane at infinity.