Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

Open maps of chainable continua


Author: Ira Rosenholtz
Journal: Proc. Amer. Math. Soc. 42 (1974), 258-264
MSC: Primary 54F20; Secondary 54C10
MathSciNet review: 0331346
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: It is apparently ``well known'' that the image of the closed unit interval under an open map is homeomorphic to the closed unit interval (see [13], [11], and [15]). In this paper, we generalize this result to chainable continua. In particular, the fact that the open continuous image of a chainable continuum is also chainable is proved, answering a question of A. Lelek (see [10]). This fact, as well as its proof, implies that the open continuous image of the pseudo-arc is also a pseudo-arc. An additional corollary (of the proof) is that a local homeomorphism of a chainable continuum is actually a homeomorphism. The proofs are all very elementary.


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


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 54F20, 54C10

Retrieve articles in all journals with MSC: 54F20, 54C10


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1974-0331346-8
PII: S 0002-9939(1974)0331346-8
Keywords: Open maps, chainable continua, local homeomorphisms, pseudo-arc
Article copyright: © Copyright 1974 American Mathematical Society