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A circle bundle pi:E->M is a fiber bundle whose fibers pi^(-1)(x) are circles. It may also have the structure of a principal bundle if there is an action of SO(2) that ...
A set of class representatives is a subset of X which contains exactly one element from each equivalence class.
Classical algebraic geometry is the study of algebraic varieties, both affine varieties in C^n and projective algebraic varieties in CP^n. The original motivation was to ...
The classification of a collection of objects generally means that a list has been constructed with exactly one member from each isomorphism type among the objects, and that ...
A subset of a topological space is called clopen if it is both closed and open.
A compact manifold without boundary.
A map f between topological spaces that maps closed sets to closed sets. If f is bijective, then f is closed <==>f is open <==>f^(-1) is continuous, where f^(-1) denotes the ...
A linear operator A:D(A)->H from its domain D(A) into a Hilbert space H is closed if for any sequence of vectors v_n in D(A) such that v_n->v and Av_n->x as n->infty, it ...
A subset of a topological group which is closed as a subset and also a subgroup.
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