The Representation of Chainable Continua with Only Two Bonding Maps

1969 ◽  
Vol 23 (3) ◽  
pp. 653 ◽  
Author(s):  
Sam W. Young
Keyword(s):  
Chainable Continua

On weakly chainable continua

1962 ◽  
Vol 51 (3) ◽  
pp. 271-282 ◽  
Author(s):  
A. Lelek
Keyword(s):  
Chainable Continua

Some Properties of Hyperspaces with Applications to Continua Theory

1979 ◽  
Vol 31 (1) ◽  
pp. 197-210 ◽  
Author(s):  
J. Grispolakis ◽  
Sam B. Nadler ◽  
E. D. Tymchatyn
Keyword(s):  
Covering Property ◽  
University Of Houston ◽  
Chainable Continua ◽  
The University

In 1972, Lelek introduced the notion of Class (W) in his seminar at the University of Houston [see below for definitions of concepts mentioned here]. Since then there has been much interest in classifying and characterizing continua in Class (W). For example, Cook has a result [5, Theorem 4] which implies that any hereditarily indecomposible continuum is in Class (W) Read [21, Theorem 4] showed that all chainable continua are in Class (W), and Feuerbacher proved the following result:(1.1) THEOREM [7, Theorem 7]. A non-chainable circle-like continuum is in Class (W) if and only if it is not weakly chainableIn [14, 4.2 and section 6], a covering property (denoted here and in [18] by CP) was defined and studied primarily for the purpose of proving that indecomposability is a Whitney property for the class of chainable continua [14, 4.3].

Continuum-Wise Expansive Homeomorphisms

1993 ◽  
Vol 45 (3) ◽  
pp. 576-598 ◽  
Author(s):  
Hisao Kato
Keyword(s):  
Continuum Theory ◽  
Topological Dynamics ◽  
Expansive Homeomorphism ◽  
The One ◽  
Chainable Continua ◽  
The Continuum

AbstractThe notion of expansive homeomorphism is important in topological dynamics and continuum theory. In this paper, a new kind of homeomorphism will be introduced and studied, namely the continuum-wise expansive homeomorphism. The class of continuum-wise expansive homeomorphisms is much larger than the one of expansive homeomorphisms. In fact, the class of continuum-wise expansive homeomorphisms contains many important homeomorphisms which often appear in "chaotic" topological dynamics and continuum theory, but which are not expansive homeomorphisms. For example, the shift maps of Knaster's indecomposable chainable continua are continuum-wise expansive homeomorphisms, but they are not expansive homeomorphisms. Also, there is a continuum-wise expansive homeomorphism on the pseudoarc. We study several properties of continuum-wise expansive homeomorphisms. Many theorems concerning expansive homeomorphisms will be generalized to the case of continuum-wise expansive homeomorphisms.

scholarly journals Periodic homeomorphisms on chainable continua

1969 ◽  
Vol 64 (2) ◽  
pp. 197-202 ◽  
Author(s):  
Beverly Brechner
Keyword(s):  
Chainable Continua

scholarly journals Periodic homeomorphisms of chainable continua

1983 ◽  
Vol 117 (1) ◽  
pp. 81-84 ◽  
Author(s):  
Wayne Lewis
Keyword(s):  
Chainable Continua
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