Let f be a mapping (i.e., continuous transformation) of a topological space X onto a topological space Y. It is of interest to investigate the properties of X which are inherited by Y under the mapping f. In particular, if f is a homeomorphism, X and Y are topologically equivalent, so that Y will share all the topological properties of X. Hovever, under 1ess restricted oonditions on f , many of the properties such as connectedness, compactness, separability, local separability (i.e., first countability) and strong separability (i.e., second countability), etc., will be inherited by Y. In this work, we are interested in investigating some important classes of mappings: open mappings, closed mappings and perfect mappings, and in determining how the image space is affected under such mappings. These mappings play fundamental role in many studies, e.g., the theory of function of one or several complex variables. Work along these lines have been initiated by G. T. Whyburn, S. Stoilow, H. Grauert, B. Remmert and K. Stein.
| Identifer | oai:union.ndltd.org:LACETR/oai:collectionscanada.gc.ca:QMM.47601 |
| Date | January 1965 |
| Creators | Lam, Woon-Chung. |
| Contributors | Costley, C. (Supervisor) |
| Publisher | McGill University |
| Source Sets | Library and Archives Canada ETDs Repository / Centre d'archives des thèses électroniques de Bibliothèque et Archives Canada |
| Language | English |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Format | application/pdf |
| Coverage | Master of Science (Department of Mathematics) |
| Rights | All items in eScholarship@McGill are protected by copyright with all rights reserved unless otherwise indicated. |
| Relation | alephsysno: 000797209, proquestno: AAIMK00332, Theses scanned by UMI/ProQuest. |
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