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dc.contributor.advisorMinc, Piotr
dc.contributor.authorOzbolt, Joseph
dc.date.accessioned2020-07-21T14:23:01Z
dc.date.available2020-07-21T14:23:01Z
dc.date.issued2020-07-21
dc.identifier.urihttp://hdl.handle.net/10415/7358
dc.description.abstractA\v nusi\'c, Bruin, and \v Cin\v c have asked in \cite{Anusic2} which hereditarily decomposable chainable continua (HDCC) have uncountably many mutually inequivalent planar embeddings. It was noted, as per the embedding technique of John C. Mayer with the $\sin(1/x)$-curve \cite{Mayer}, that any HDCC which is the compactification of a ray with an arc likely has this property. We show here two methods for constructing $\mathfrak{c}$-many mutually inequivalent planar embeddings of the classic Knaster $V \Lambda$-continuum, $K$, also referred to here as the Knaster accordion. The first of these two methods produces $\mathfrak{c}$-many planar embeddings of $K$, all of whose images have a different set of accessible points from the image of the standard embedding of $K$, while the second method produces $\mathfrak{c}$-many embeddings of $K$ which preserve the set of accessible points of the standard embedding.en_US
dc.subjectMathematics and Statisticsen_US
dc.titleOn Planar Embeddings of the Knaster V Lambda-Continuumen_US
dc.typePhD Dissertationen_US
dc.embargo.lengthen_US
dc.embargo.statusNOT_EMBARGOEDen_US


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