English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

The main result of this paper is the following theorem. Let { Xa, fO, a, /8 E I) be an inverse system of compact Hausdorff spaces and continuous onto maps with inverse limit X. Letp E X and A be closed in X. There exists a continuum neighborhood of p disjoint from A if and only if there exists a E I and disjoint sets U and V open in X,, neighborhoods respectively of p a,faX'(U) lies in a single component of X fl'(V). This is Theorem B of the text. Introduction. Throughout this paper the conventions and elementary results on inverse limits of topological spaces are those given in Bourbaki [3] except when noted otherwise. (I, A) is a directed set, { X, a C I) is a collection of nonvoid compact Hausdorff spaces and, for every pair (a, /3) where a a(} denotes an inverse system of subcontinua if and only if for all /3 > a, W,B is a subcontinuum of X,,, and ( W,f,fafI Wf) is an inverse system. Let S be a compact Hausdorff space. The following dictionary provides translations of some common properties of S into properties of the set function T defined on {A IA c S}. Received by the editors September 29, 1975 and, in revised form, July 26, 1976. AMS (MOS) subject classifications (1970). Primary 54F15; Secondary 54B25.

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