Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Disk-like products of $\lambda$ connected continua. II


Author: Charles L. Hagopian
Journal: Proc. Amer. Math. Soc. 52 (1975), 479-484
MSC: Primary 54F20
DOI: https://doi.org/10.1090/S0002-9939-1975-0494000-9
MathSciNet review: 0494000
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: R. H. Bing [3] proved that every atriodic, hereditarily decomposable, hereditarily unicoherent continuum is arc-like. Using this theorem, the author [5] showed that $\lambda$ connected continua $X$ and $Y$ are arc-like when the topological product $X \times Y$ is disk-like. In this paper we consider products that have a more general mapping property. Suppose that $X$ and $Y$ are $\lambda$ connected continua and that for each $\varepsilon > 0$, there exists an $\varepsilon$-map of $X \times Y$ into the plane. Then $X$ is either arc-like or circle-like. Furthermore, if $X$ is circle-like, then $Y$ is arc-like. Hence $X \times Y$ is either disk-like or annulus-like.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 54F20

Retrieve articles in all journals with MSC: 54F20


Additional Information

Keywords: Chainable continua, snake-like continua, disk-like product, arc-like continua, lambda connectivity, hereditarily decomposable continua, arcwise connectivity, triod, unicoherence, circle-like continua, <!– MATH $\varepsilon$ –> <IMG WIDTH="15" HEIGHT="20" ALIGN="BOTTOM" BORDER="0" SRC="images/img1.gif" ALT="$\varepsilon$">-map into the plane
Article copyright: © Copyright 1975 American Mathematical Society