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Full-Text Articles in Mathematics
Planarity Of Whitney Levels, Jorbe Bustamante, W. J. Charatonik, Raul Escobedo
Planarity Of Whitney Levels, Jorbe Bustamante, W. J. Charatonik, Raul Escobedo
Mathematics and Statistics Faculty Research & Creative Works
First, we characterize all locally connected continua whose all Whitney levels are planar. Second, we show by example that planarity is not a (strong) Whitney reversible property. This answers a question from Illanes-Nadler book [2].
Property Of Kelley For The Cartesian Products And Hyperspaces, W. J. Charatonik, J. J. Charatonik
Property Of Kelley For The Cartesian Products And Hyperspaces, W. J. Charatonik, J. J. Charatonik
Mathematics and Statistics Faculty Research & Creative Works
A continuum X having the property of Kelley is constructed such that neither X × [0, 1], nor the hyperspace C(X), nor small Whitney levels in C(X) have the property of Kelley. This answers several questions asked in the literature.
A Degree Of Nonlocal Connectedness, J. J. Charatonik, W. J. Charatonik
A Degree Of Nonlocal Connectedness, J. J. Charatonik, W. J. Charatonik
Mathematics and Statistics Faculty Research & Creative Works
To any continuum X weassign an ordinal number (or the symbol ∞) s(X), called the degree of nonlocal connectedness of X. We show that (1) the degree cannot be increased under continuous surjections; (2) for hereditarily unicoherent continua X, the degree of a subcontinuum of X is less than or equal to s(X); (3) s(C(X)) ≤ s(X), where C(X) denotes the hyperspace of subcontinua of a continuum X. We also investigate the degrees of Cartesian products and inverse limits. As an application weconstruct an uncountable family of metric continua X homeomorphic to C(X).
Openness And Monotoneity Of Induced Mappings, W. J. Charatonik
Openness And Monotoneity Of Induced Mappings, W. J. Charatonik
Mathematics and Statistics Faculty Research & Creative Works
It is shown that for locally connected continuum X if the induced mapping C(f) : C(X) ->C(Y) is open, then f is monotone. As a corollary it follows that if the continuum X is hereditarily locally connected and C(f) is open, then f is a homeomorphism. An example is given to show that local connectedness is essential in the result.