Cardinality of Pseudo-Endpoints of Chainable Continua

Date

2017-12-13

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Abstract

A point x in a nondegenerate chainable continuum X is a pseudo-endpoint if for each neighborhood U of x and for each epsilon > 0 there is an epsilon-chain C covering X, such that C_1 is in U. This property was originally discussed by R. H. Bing(1951). We construct nondegenerate chainable continua with (m, n) number of endpoints and pseudo-endpoints respectively in Chapter 2. Furthermore, we use inverse limits and atomic maps to construct continua with countable and uncountable sets of pseudo- endpoints.


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Keywords

Pseudo-endpoint, Chainable Continuum

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