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Proper Manors TV
Proper may refer to: Mathematics * Proper map, in topology, a property of continuous function between topological spaces, if inverse images of compact subsets are compact * Proper morphism, in algebraic geometry, an analogue of a proper map for algebraic varieties * Proper transfer function, a transfer function in control theory in which the degree of the numerator does not exceed the degree of the denominator * Proper equilibrium, in game theory, a refinement of the Nash equilibrium * Proper subset * Proper space * Proper class * Proper complex random variable Other uses * Proper (liturgy), the part of a Christian liturgy that is specific to the date within the Liturgical Year * Proper frame, such system of reference in which object is stationary (non moving), sometimes also called a co-moving frame * Proper (heraldry), in heraldry, means depicted in natural colors * Proper Records, a UK record label * ''Proper'' (album), an album by Into It. Over It. released in 2011 * Pro ...
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Proper Map
In mathematics, a function (mathematics), function between topological spaces is called proper if inverse images of compact space, compact subsets are compact. In algebraic geometry, the analogous concept is called a proper morphism. Definition There are several competing definitions of a "proper Function (mathematics), function". Some authors call a function f : X \to Y between two topological spaces if the preimage of every Compact space, compact set in Y is compact in X. Other authors call a map f if it is continuous and ; that is if it is a Continuous map, continuous closed map and the preimage of every point in Y is Compact set, compact. The two definitions are equivalent if Y is Locally compact space, locally compact and Hausdorff space, Hausdorff. Let f : X \to Y be a closed map, such that f^(y) is compact (in X) for all y \in Y. Let K be a compact subset of Y. It remains to show that f^(K) is compact. Let \left\ be an open cover of f^(K). Then for all k \in K this is ...
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