On the first homology of Peano continua

Gregory R. Conner; Samuel M. Corson

doi:10.4064/fm232-1-3

On the first homology of Peano continua

Fundamenta Mathematicae ◽

10.4064/fm232-1-3 ◽

2016 ◽

Vol 232 (1) ◽

pp. 41-48 ◽

Cited By ~ 1

Author(s):

Gregory R. Conner ◽

Samuel M. Corson

Keyword(s):

Peano Continua

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The nonexistence of expansive Zn actions on Peano continua that contain no θ-curves

Topology and its Applications ◽

10.1016/j.topol.2006.06.005 ◽

2007 ◽

Vol 154 (2) ◽

pp. 462-468 ◽

Cited By ~ 3

Author(s):

Enhui Shi ◽

Lizhen Zhou ◽

Youcheng Zhou

Keyword(s):

Peano Continua

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Deforestation of Peano continua and minimal deformation retracts

Topology and its Applications ◽

10.1016/j.topol.2012.07.001 ◽

2012 ◽

Vol 159 (15) ◽

pp. 3253-3262 ◽

Cited By ~ 5

Author(s):

G. Conner ◽

M. Meilstrup

Keyword(s):

Peano Continua

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Simple Links in Locally Compact Connected Hausdorff Spaces are Nondegenerate

Canadian Journal of Mathematics ◽

10.4153/cjm-1982-022-2 ◽

1981 ◽

Vol 34 (2) ◽

pp. 349-355

Author(s):

David John

Keyword(s):

Hausdorff Space ◽

Metric Spaces ◽

Connected Space ◽

Hausdorff Spaces ◽

Locally Compact ◽

Peano Continua

The fact that simple links in locally compact connected metric spaces are nondegenerate was probably first established by C. Kuratowski and G. T. Whyburn in [2], where it is proved for Peano continua. J. L. Kelley in [3] established it for arbitrary metric continua, and A. D. Wallace extended the theorem to Hausdorff continua in [4]. In [1], B. Lehman proved this theorem for locally compact, locally connected Hausdorff spaces. We will show that the locally connected property is not necessary.A continuum is a compact connected Hausdorff space. For any two points a and b of a connected space M, E(a, b) denotes the set of all points of M which separate a from b in M. The interval ab of M is the set E(a, b) ∪ {a, b}.

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