المستودع الأكاديمي جامعة المدينة

An intrinsic codimension two cellular decomposition of the Hilbert cube

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dc.contributor Garity, Dennis J
dc.contributor Solmon, Donald
dc.contributor Dray, Tevian
dc.contributor Bogley, William
dc.contributor Zhang, Eugene
dc.date 2007-08-01T23:17:58Z
dc.date 2007-08-01T23:17:58Z
dc.date 2007-07-12
dc.date 2007-08-01T23:17:58Z
dc.date.accessioned 2013-10-16T08:04:27Z
dc.date.available 2013-10-16T08:04:27Z
dc.date.issued 2013-10-16
dc.identifier http://hdl.handle.net/1957/6259
dc.identifier.uri http://koha.mediu.edu.my:8181/xmlui/handle/1957/6259
dc.description Graduation date: 2008
dc.description Cellular sets in the Hilbert cube are the intersection of nested sequences of normal cubes. One way of getting cellular maps on the Hilbert cube is by decomposing the Hilbert cube into cellular sets and using a quotient map. By using a cellular decomposition of the Hilbert cube, an example of a cellular map is given to show that the image of the Hilbert cube under a cellular map can have complex non manifold part, not be a Hilbert cube manifold, and still be a Hilbert cube manifold factor. The non degenerate decomposition elements are shown to satisfy the cellularity criteria. To measure how far the image is from being a Hilbert cube manifold, the idea of covering codimension in finite dimensions is generalized by using a homological codimension approach. In finite dimensional settings, the two codimensions are equivalent. The complexity of the non manifold part of the image space is measured in terms of intrinsic codimension, which uses the homological codimension of the image of the union of nondegenerate decomposition elements. The intrinsic codimension of the map in this example is found to be exactly two. Using a characterization of Hilbert cube manifolds, it is shown that the decomposition space is not the Hilbert cube, but is a factor of the Hilbert cube.
dc.language en_US
dc.subject Hilbert Cube
dc.subject Intrinsic Codimension
dc.subject Homological Codimension
dc.subject Geometrically Central
dc.subject Interior Essential
dc.subject Mathematics
dc.title An intrinsic codimension two cellular decomposition of the Hilbert cube
dc.type Thesis


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