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On homeomorphisms of the density type topologies

100%
Filipczak M., Hejduk J., Wilczyński W.
Commentationes Mathematicae
|
2005
|
tom 45
|
nr 2
EN
This paper is dealing of the homeomorphisms of the density type topologies introduced in [3].
2
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Topological entropy on zero-dimensional spaces

100%
Bobok J., Zindulka O.
Fundamenta Mathematicae
|
1999
|
tom 162
|
nr 3
233-249
EN
Let X be an uncountable compact metrizable space of topological dimension zero. Given any a ∈[0,∞] there is a homeomorphism on X whose topological entropy is a.
3
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Strongly chaotic dendrites

75%
Charatonik J. J., Charatonik W. J.
Colloquium Mathematicum
|
1996
|
tom 70
|
nr 2
181-190
EN
The concept of a strongly chaotic space is introduced, and its relations to chaotic, rigid and strongly rigid spaces are studied. Some sufficient as well as necessary conditions are shown for a dendrite to be strongly chaotic.
4
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Generalized Alexandroff Duplicates and CD 0(K) spaces

75%
Çaglar M., Ercan Z., Polat F.
Open Mathematics
|
2006
|
tom 4
|
nr 3
371-375
EN
We define and investigateCD Σ,Γ(K, E)-type spaces, which generalizeCD 0-type Banach lattices introduced in [1]. We state that the space CD Σ,Γ(K, E) can be represented as the space of E-valued continuous functions on the generalized Alexandroff Duplicate of K. As a corollary we obtain the main result of [6, 8].
5
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Hereditarily weakly confluent induced mappings are homeomorphisms

51%
Charatonik J. J., Charatonik W. J.
Colloquium Mathematicum
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1998
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tom 75
|
nr 2
195-203
EN
For a given mapping f between continua we consider the induced mappings between the corresponding hyperspaces of closed subsets or of subcontinua. It is shown that if either of the two induced mappings is hereditarily weakly confluent (or hereditarily confluent, or hereditarily monotone, or atomic), then f is a homeomorphism, and consequently so are both the induced mappings. Similar results are obtained for mappings between cones over the domain and over the range continua.
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