Inverse Limit Spaces

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Inverse systems, inverse limit spaces, and bonding maps are defined. An investigation of the properties that an inverse limit space inherits, depending on the conditions placed on the factor spaces and bonding maps is made. Conditions necessary to ensure that the inverse limit space is compact, connected, locally connected, and semi-locally connected are examined. A mapping from one inverse system to another is defined and the nature of the function between the respective inverse limits, induced by this mapping, is investigated. Certain restrictions guarantee that the induced function is continuous, onto, monotone, periodic, or open. It is also shown that ... continued below

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v, 107 leaves

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Williams, Stephen Boyd December 1974.

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This thesis is part of the collection entitled: UNT Theses and Dissertations and was provided by UNT Libraries to Digital Library, a digital repository hosted by the UNT Libraries. It has been viewed 19 times . More information about this thesis can be viewed below.

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  • Williams, Stephen Boyd

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Inverse systems, inverse limit spaces, and bonding maps are defined. An investigation of the properties that an inverse limit space inherits, depending on the conditions placed on the factor spaces and bonding maps is made. Conditions necessary to ensure that the inverse limit space is compact, connected, locally connected, and semi-locally connected are examined.
A mapping from one inverse system to another is defined and the nature of the function between the respective inverse limits, induced by this mapping, is investigated. Certain restrictions guarantee that the induced function is continuous, onto, monotone, periodic, or open. It is also shown that any compact metric space is the continuous image of the cantor set.
Finally, any compact Hausdorff space is characterized as the inverse limit of an inverse system of polyhedra.

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v, 107 leaves

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  • December 1974

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  • June 24, 2015, 9:39 a.m.

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  • Aug. 10, 2016, 10:33 p.m.

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Williams, Stephen Boyd. Inverse Limit Spaces, thesis, December 1974; Denton, Texas. (digital.library.unt.edu/ark:/67531/metadc663483/: accessed October 16, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; .