Geodesic
Completely Regular Mappings and Homogeneous, Aposyndetic Continua
Canadian journal of mathematics, Tome 33 (1981) no. 2, pp. 450-453

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The purpose of this note is to prove an improved version of Jones' Aposyndetic Decomposition Theorem. Corollaries to the new theorem re-emphasize the importance of understanding aposyndetic, homogeneous continua.The proof is a synthesis of results about homogeneous continua with results from an unexpected source: completely regular mappings. Completely regular mappings occur naturally and often in the study of homogeneous continua, which is a surprising and pleasing phenomenon, since these mappings were invented for quite another purpose [1]. The author believes that these maps are likely to provide even more new information about homogeneous continua.A continuum is a compact, connected, nonvoid metric space. A curve is a one-dimensional continuum. A continuum M is homogeneous if for each pair of points p and q belonging to M, there exists a homeomorphism h: M → M such that h(p) = q. 
Jr., James T. Rogers. Completely Regular Mappings and Homogeneous, Aposyndetic Continua. Canadian journal of mathematics, Tome 33 (1981) no. 2, pp. 450-453. doi: 10.4153/CJM-1981-039-4
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