Compact Hausdorff

Some articles on compact, hausdorff, compact hausdorff:

Extremally Disconnected Space
... An extremally disconnected space that is also compact and Hausdorff is sometimes called a Stonean space ... which is usually a totally disconnected compact Hausdorff space.) A theorem due to Andrew Gleason says that the projective objects of the category of compact Hausdorff spaces are ... An extremally disconnected first countable collectionwise Hausdorff space must be discrete ...
Bohr Compactification - Definitions and Basic Properties
... a topological group G, the Bohr compactification of G is a compact Hausdorff topological group Bohr(G) and a continuous homomorphism b G → Bohr(G) which is universal with respect to ... problems in the theory of almost periodic functions on topological groups to that of functions on compact groups ... only if the set of right translates gf where is relatively compact in the uniform topology as g varies through G ...
Baire Set - More General Definitions
... According to (Halmos 1950, page 220), a subset of a locally compact Hausdorff topological space is called a Baire set if it belongs to the smallest σ–ring containing all compact Gδ sets ... A discrete topological space is locally compact and Hausdorff ... However, since the compact subspaces of a discrete space are precisely the finite subspaces, the Baire sets, according to Halmos, are precisely the at most countable sets ...
More About Closed Sets
... However, the compact Hausdorff spaces are "absolutely closed", in the sense that, if you embed a compact Hausdorff space K in an arbitrary Hausdorff ... a process that turns a completely regular Hausdorff space into a compact Hausdorff space, may be described as adjoining limits of certain nonconvergent nets to the space ... Furthermore, every closed subset of a compact space is compact, and every compact subspace of a Hausdorff space is closed ...

Famous quotes containing the word compact:

    What compact mean you to have with us?
    Will you be pricked in number of our friends,
    Or shall we on, and not depend on you?
    William Shakespeare (1564–1616)