Some articles on continuous map, map, continuous, maps:
Stone–Čech Compactification - Universal Property and Functoriality
... X is a compact Hausdorff space together with a continuous map from X and has the following universal property any continuous map f X → K, where K is a compact Hausdorff space, lifts uniquely to a ... starting space be Tychonoff (or even locally compact Hausdorff), for the following reasons The map from X to its image in βX is a homeomorphism if and only if X is Tychonoff ... The map from X to its image in βX is a homeomorphism to an open subspace if and only if X is locally compact Hausdorff ...
... X is a compact Hausdorff space together with a continuous map from X and has the following universal property any continuous map f X → K, where K is a compact Hausdorff space, lifts uniquely to a ... starting space be Tychonoff (or even locally compact Hausdorff), for the following reasons The map from X to its image in βX is a homeomorphism if and only if X is Tychonoff ... The map from X to its image in βX is a homeomorphism to an open subspace if and only if X is locally compact Hausdorff ...
Sheaf (mathematics) - The étalé Space of A Sheaf
... For example, if F is the sheaf of sections of a continuous function f Y → X, then E = Y if and only if f is a local homeomorphism ... As a set, it is their disjoint union and π is the obvious map that takes the value x on the stalk of F over x ∈ X ... Two morphisms between sheaves determine a continuous map of the corresponding étalé spaces that is compatible with the projection maps (in the sense that every germ is mapped ...
... For example, if F is the sheaf of sections of a continuous function f Y → X, then E = Y if and only if f is a local homeomorphism ... As a set, it is their disjoint union and π is the obvious map that takes the value x on the stalk of F over x ∈ X ... Two morphisms between sheaves determine a continuous map of the corresponding étalé spaces that is compatible with the projection maps (in the sense that every germ is mapped ...
Complete Heyting Algebra - Frames and Locales
... those of Frm, and they are usually called maps (of locales) ... The relation of locales and their maps to topological spaces and continuous functions may be seen as follows ... Let be any map ...
... those of Frm, and they are usually called maps (of locales) ... The relation of locales and their maps to topological spaces and continuous functions may be seen as follows ... Let be any map ...
Lefschetz Fixed-point Theorem - Relation To The Brouwer Fixed Point Theorem
... the Brouwer fixed point theorem, which states that every continuous map from the n-dimensional closed unit disk Dn to Dn must have at least one fixed point ... as follows Dn is compact and triangulable, all its homology groups except H0 are 0, and every continuous map f Dn → Dn induces a non-zero homomorphism f* H0(Dn, Q) → H0(Dn, Q) all this ...
... the Brouwer fixed point theorem, which states that every continuous map from the n-dimensional closed unit disk Dn to Dn must have at least one fixed point ... as follows Dn is compact and triangulable, all its homology groups except H0 are 0, and every continuous map f Dn → Dn induces a non-zero homomorphism f* H0(Dn, Q) → H0(Dn, Q) all this ...
Famous quotes containing the words map and/or continuous:
“A map of the world that does not include Utopia is not worth even glancing at, for it leaves out the one country at which Humanity is always landing.”
—Oscar Wilde (1854–1900)
“The problem, thus, is not whether or not women are to combine marriage and motherhood with work or career but how they are to do so—concomitantly in a two-role continuous pattern or sequentially in a pattern involving job or career discontinuities.”
—Jessie Bernard (20th century)
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