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)

 

Relationships between continuum neighborhoods in inverse limit spaces and separations in inverse limit sequences


Author: Harvey S. Davis
Journal: Proc. Amer. Math. Soc. 64 (1977), 149-153
MSC: Primary 54B25; Secondary 54F20
MathSciNet review: 0442876
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The main result of this paper is the following theorem. Let $ \{ {X_\alpha },{f_{\alpha \beta }},\alpha ,\beta \in I\} $ be an inverse system of compact Hausdorff spaces and continuous onto maps with inverse limit X. Let $ p \in X$ and A be closed in X. There exists a continuum neighborhood of p disjoint from A if and only if there exists $ \alpha \in I$ and disjoint sets U and V open in $ {X_\alpha }$, neighborhoods respectively of $ {p_\alpha }$ and $ {A_\alpha }$ such that for all $ \beta \geqslant \alpha ,f_{\alpha \beta }^{ - 1}(U)$ lies in a single component of $ {X_\beta } - f_{\alpha \beta }^{ - 1}(V)$. This is Theorem B of the text.


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


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 54B25, 54F20

Retrieve articles in all journals with MSC: 54B25, 54F20


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1977-0442876-5
PII: S 0002-9939(1977)0442876-5
Keywords: Continuum neighborhood, set function T, inverse limit, compact Hausdorff space
Article copyright: © Copyright 1977 American Mathematical Society