2014
DOI: 10.1134/s0037446614020128
|View full text |Cite
|
Sign up to set email alerts
|

The shark teeth is a topological IFS-attractor

Abstract: We show that the space called shark teeth is a topological IFSattractor, that is for every open cover of X = n i=1 f i (X), its image under every suitable large composition from the family of continuous functions {f 1 , ..., fn} lies in some set from the cover. In particular, there exists a space which is not homeomorphic to any IFS-attractor but is a topological IFSattractor.2010 Mathematics Subject Classification. Primary 28A80; 54D05; 54F50; 54F45.

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...
2
1
1
1

Citation Types

0
10
0

Year Published

2015
2015
2020
2020

Publication Types

Select...
6

Relationship

0
6

Authors

Journals

citations
Cited by 12 publications
(10 citation statements)
references
References 5 publications
0
10
0
Order By: Relevance
“…In other words, this is not a Banach fractal. However, it can be still shown that this is a topological fractal, which was proved in [17], though we contribute a shorter proof next.…”
Section: From (B) Both Sides Of This Inequality Become Positive Somentioning
confidence: 79%
See 1 more Smart Citation
“…In other words, this is not a Banach fractal. However, it can be still shown that this is a topological fractal, which was proved in [17], though we contribute a shorter proof next.…”
Section: From (B) Both Sides Of This Inequality Become Positive Somentioning
confidence: 79%
“…Recall that by a Peano continuum, we understand a continuous image of the closed unit interval [0, 1]. The space presented next was firstly constructed in [3], and studied later in [17].…”
Section: From (B) Both Sides Of This Inequality Become Positive Somentioning
confidence: 99%
“…also [23]) it was proved that each Peano continuum with free open arc is the fractal of some TIFS. Our second example (I Â P) shows that there is a wide class of Peano continua without free arc which are attractors of some TGIFSs.…”
Section: Topologically Contracting Gifssmentioning
confidence: 99%
“…Over the years, an interest in non-contractive IFSs has grown, e.g., [1,5,10,16,17,19,20]. Various kinds of attractors for possibly discontinuous IFSs were offered using the language of multivalued maps, e.g., [11,[13][14][15].…”
Section: Introductionmentioning
confidence: 99%