|
In the mathematical field of point-set topology, a continuum (plural: "continua") is a nonempty compact connected metric space, or, less frequently, a compact connected Hausdorff space. Continuum theory is the branch of topology devoted to the study of continua. == Definitions == * A continuum that contains more than one point is called nondegenerate. * A subset ''A'' of a continuum ''X'' such that ''A'' itself a continuum is called a subcontinuum of ''X''. A space homeomorphic to a subcontinuum of the Euclidean plane R2 is called a planar continuum. * A continuum ''X'' is homogeneous if for every two points ''x'' and ''y'' in ''X'', there exists a homeomorphism ''h'': ''X'' → ''X'' such that ''h''(''x'') = ''y''. * A Peano continuum is a continuum that is locally connected at each point. * An indecomposable continuum is a continuum that cannot be represented as the union of two proper subcontinua. A continuum ''X'' is hereditarily indecomposable if every subcontinuum of ''X'' is indecomposable. * The dimension of a continuum usually means its topological dimension. A one-dimensional continuum is often called a curve. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Continuum (topology)」の詳細全文を読む スポンサード リンク
|