Mathematical Sciences: Problems in Set-Theoretic Topology
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Set-theoretic topology is a branch of topology in which set-            theoretic techniques are used to solve problems about abstract                  spaces.  In it, special axioms (such as Godel's Axiom of                        Constructibility, Martin's Axiom, the covering Lemma, and the                   Product Measure Extension Axiom), forcing techniques, and other                 set-theoretic tools are used to clarify, and often solve, long-                 outstanding problems, and through consistency results to isolate                and identify topological properties worthy of study.  The                       principal investigator will continue his research in this branch,               centered on four areas where recent results have greatly enhanced               our understanding of the spaces in question and, in some cases,                 the set-theoretic tools themselves.  The spaces in question are                 various classes of countably compact spaces; Frechet chain net                  spaces; nonmetrizable manifolds; and countably metacompact                      spaces.  Such studies will probably have less immediate                         application than more geometric topological studies but in the                  long run can be expected to influence our ideas about space and                 even about the nature of proof.
{'FirstName': 'Peter', 'LastName': 'Nyikos', 'PI_MID_INIT': 'J', 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Peter J Nyikos', 'EmailAddress': 'nyikos@math.sc.edu', 'NSF_ID': '000222723', 'StartDate': '07/01/1987', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
{'Name': 'University of South Carolina at Columbia', 'CityName': 'COLUMBIA', 'ZipCode': '292083403', 'PhoneNumber': '8037777093', 'StreetAddress': '1600 HAMPTON ST', 'StreetAddress2': None, 'CountryName': 'United States', 'StateName': 'South Carolina', 'StateCode': 'SC', 'CONGRESSDISTRICT': '06', 'CONGRESS_DISTRICT_ORG': 'SC06', 'ORG_UEI_NUM': 'J22LNTMEDP73', 'ORG_LGL_BUS_NAME': 'UNIVERSITY OF SOUTH CAROLINA', 'ORG_PRNT_UEI_NUM': 'J22LNTMEDP73'}
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{'Code': '1267', 'Text': 'TOPOLOGY'}
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