Strong size properties

Macı́as, Sergio; Piceno, César

doi:10.3336/gm.48.1.10

Search citation statements

Order By: Relevance

Paper Sections

Select...

Definitions and Notation1

Introduction1

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2015

2022

Publication Types

Select...

Article5

Book1

Relationship

Self Cite1

Independent5

Authors

Journals

Cited by 7 publications

(2 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Observe that µ ′ is a strong size map for S. Hence, by [17,Theorem 5.4], there exists a strong size map µ :…”

Section: Definitions and Notationmentioning

confidence: 99%

See 1 more Smart Citation

More on strong size properties

Macı́as

Piceno

2015

Glas. Mat. Ser. III

Self Cite

View full text Add to dashboard Cite

Abstract. We continue our study of strong size maps. We show that strong size levels for the n-fold hyperspace of a continuum contain (n − 1)-cells. We give two constructions of strong size maps. We introduce reversible strong size properties. We prove that each of the following properties: being a continuum chainable continuum, being a locally connected continuum, and being a continuum with the property of Kelley, is a reversible strong size property. Following Professors Goodykoontz and Nadler, we define admissible strong size maps and show that the levels of admissible strong size maps for the n-fold hyperspace of a locally connected continuum are homeomorphic to the Hilbert cube. Professor Benjamín Espinoza defined Whitney preserving maps for the hyperspace of subcontinua of a continuum. We define strong size preserving maps and show that this class of maps coincides with the class of homeomorphisms.

show abstract

“…Observe that µ ′ is a strong size map for S. Hence, by [17,Theorem 5.4], there exists a strong size map µ :…”

Section: Definitions and Notationmentioning

confidence: 99%

“…We continue our study of strong size maps ( [17]). Professor H. Hosokawa defines strong size maps for the n-fold hyperspace of a continuum X in [11] as a natural generalization of a Whitney map for the hyperspace of subcontinua of X.…”

Section: Introductionmentioning

confidence: 99%