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1
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A decomposition theorem for a class of continua for which the set function T is continuous

100%
Macías S.
Colloquium Mathematicum
|
2007
|
tom 109
|
nr 1
163-170
EN
We prove a decomposition theorem for a class of continua for which F. B.. Jones's set function 𝓣 is continuous. This gives a partial answer to a question of D. Bellamy.
2
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Absolute n-fold hyperspace suspensions

63%
Macías S., Nadler S.
Colloquium Mathematicum
|
2006
|
tom 105
|
nr 2
221-231
EN
The notion of an absolute n-fold hyperspace suspension is introduced. It is proved that these hyperspaces are unicoherent Peano continua and are dimensionally homogeneous. It is shown that the 2-sphere is the only finite-dimensional absolute 1-fold hyperspace suspension. Furthermore, it is shown that there are only two possible finite-dimensional absolute n-fold hyperspace suspensions for each n ≥ 3 and none when n = 2. Finally, it is shown that infinite-dimensional absolute n-fold hyperspace suspensions must be unicoherent Hilbert cube manifolds.
3
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The set functions 𝓣 and 𝒦 and irreducible continua

63%
Fernández L., Macías S.
Colloquium Mathematicum
|
2010
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tom 121
|
nr 1
79-91
EN
We study the set functions 𝓣 and 𝒦 on irreducible continua. We present several properties of these functions when defined on irreducible continua. In particular, we characterize the class of irreducible continua for which these functions are continuous. We also characterize the class of 𝒦-symmetric irreducible continua.
4
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1/2-Homogeneous hyperspace suspensions

63%
Macías S., Pellicer-Covarrubias P.
Colloquium Mathematicum
|
2012
|
tom 128
|
nr 1
109-132
EN
We continue the study of 1/2-homogeneity of the hyperspace suspension of continua. We prove that if X is a decomposable continuum and its hyperspace suspension is 1/2-homogeneous, then X must be continuum chainable. We also characterize 1/2-homogeneity of the hyperspace suspension for several classes of continua, including: continua containing a free arc, atriodic and decomposable continua, and decomposable irreducible continua about a finite set.
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