Compact Hausdorff Space

Some articles on compact hausdorff space, hausdorff, compact, space, spaces, compact hausdorff spaces:

Finite Intersection Property - Applications
... Let X be a compact Hausdorff space that satisfies the property that no one-point set is open ... We cannot eliminate the Hausdorff condition a countable set with the indiscrete topology is compact, has more than one point, and satisfies the property that no one ... that one point sets cannot be open as a finite space given the discrete topology shows ...
Arzelà–Ascoli Theorem - Generalizations - Compact Metric Spaces and Compact Hausdorff Spaces
... can be generalized to the setting of arbitrary compact metric spaces and, more generally still, compact Hausdorff spaces ... Let X be a compact Hausdorff space, and let C(X) be the space of real-valued continuous functions on X ... bounded if for every x ∈ X, A version of this holds also in the space C(X) of real-valued continuous functions on a compact Hausdorff space X (Dunford Schwartz 1958, §IV.6.7) Let X be ...
Stone–Čech Compactification
... compactification is a technique for constructing a universal map from a topological space X to a compact Hausdorff space βX ... The Stone–Čech compactification βX of a topological space X is the largest compact Hausdorff space "generated" by X, in the sense that any map from X to a ... If X is a Tychonoff space then the map from X to its image in βX is a homeomorphism, so X can be thought of as a (dense) subspace of βX ...

Famous quotes containing the words space and/or compact:

    Why not a space flower? Why do we always expect metal ships?
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    The powers of the federal government ... result from the compact to which the states are parties, [and are] limited by the plain sense and intention of the instrument constituting that compact.
    James Madison (1751–1836)