Continuous Mappings and Some New Classes of Spaces
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Ohio University / OhioLINK
2009
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ndltd-OhioLink-oai-etd.ohiolink.edu-ohiou12393875552021-08-03T05:45:57Z Continuous Mappings and Some New Classes of Spaces Stover, Derrick D. Mathematics continuous mapping general topology continuous functions mappings strongly-d-separable spaces perfect mapping Tychonoff space open continuous mapping metrizable <p>The theory of continuous mappings is a crucial field of study in general topology. In this dissertation we expand on this vast area by considering continuous functions and some new classes of spaces, while also pursuing other natural considerations in this direction.</p><p>A space X is said to be π-metrizable if it has a σ-discrete π-base. The behavior of π-metrizable spaces under certain types of mappings is studied. In particular we characterize strongly-d-separable spaces as those which are the image of a π-metrizable space under a perfect mapping. Each Tychonoff space can be represented as the image of a π-metrizable space under an open continuous mapping. A question posed by Arhangel'skii regarding if a π-metrizable topological group must be metrizable receives a negative answer.</p><p>A space X is said to be coconnected if |X|>1 and for every connected subset C, XC is connected. It is established that every coconnected space can be mapped onto a coconnected compactum by a continuous bijection. Also every coconnected compactum is the union of two linearly ordered continua intersecting only at end points. In particular every separable compact coconnected space is homeomorphic to the circumference. Every continuum that is cleavable over the class of coconnected spaces together with the class of LOTS embeds into a coconnected space. Thus cleavability of continua over the class of LOTS can be generalized to cleavability over coconnected spaces and their connected subsets. </p><p>Cleavability over linearly ordered spaces has been an important direction of study. We establish that every locally connected, connected space cleavable over the class of LOTS is linearly ordered. Every separable connected space cleavable over R condenses onto an interval. Finally it is shown that every space cleavable over the class of LOTS containing a converging sequence has a cut point.</p> 2009-08-11 English text Ohio University / OhioLINK http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1239387555 http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1239387555 unrestricted This thesis or dissertation is protected by copyright: all rights reserved. It may not be copied or redistributed beyond the terms of applicable copyright laws. |
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NDLTD |
| language |
English |
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NDLTD |
| topic |
Mathematics continuous mapping general topology continuous functions mappings strongly-d-separable spaces perfect mapping Tychonoff space open continuous mapping metrizable |
| spellingShingle |
Mathematics continuous mapping general topology continuous functions mappings strongly-d-separable spaces perfect mapping Tychonoff space open continuous mapping metrizable Stover, Derrick D. Continuous Mappings and Some New Classes of Spaces |
| author |
Stover, Derrick D. |
| author_facet |
Stover, Derrick D. |
| author_sort |
Stover, Derrick D. |
| title |
Continuous Mappings and Some New Classes of Spaces |
| title_short |
Continuous Mappings and Some New Classes of Spaces |
| title_full |
Continuous Mappings and Some New Classes of Spaces |
| title_fullStr |
Continuous Mappings and Some New Classes of Spaces |
| title_full_unstemmed |
Continuous Mappings and Some New Classes of Spaces |
| title_sort |
continuous mappings and some new classes of spaces |
| publisher |
Ohio University / OhioLINK |
| publishDate |
2009 |
| url |
http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1239387555 |
| work_keys_str_mv |
AT stoverderrickd continuousmappingsandsomenewclassesofspaces |
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1719424948676591616 |