ON TOPOLOGICAL STRUCTURE OF SPACES THAT ARE MILDLY CONNECTED-CLEAVABLE OVER THE REALS

A.V. ARHANGEL’SKII

doi:10.32219/isms.70.2_233

著者情報

キーワード: Network-connectedness, π-connected space, Connected space, locally connected, space, Cleavability, Punctured closed connected set, mildly connected-cleavable space, 1-manifold, Baire, property, Moore space, Complete metric space

ジャーナルフリー

2009 年 70 巻 2 号 p. 233-238

DOI https://doi.org/10.32219/isms.70.2_233

詳細

抄録

We prove the following theorem (8): If X is a nowhere hereditarily disconnected homogeneous space metrizable by a complete metric, and X is cleavable over R along every punctured closed connected subset, then X is locally connected. Using this result, we establish the next theorem (Theorem 15): Suppose that X is an infinite homogeneous connected locally compact metrizable space. Suppose also that X is cleavable over R along every punctured closed connected subset. Then X is homeomorphic to the space R of real numbers.

責任著者(Corresponding author)

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