On mobs with certain group-like properties
| dc.contributor.author | Chew, James Francis | en |
| dc.contributor.department | Mathematics | en |
| dc.date.accessioned | 2019-10-10T19:28:01Z | en |
| dc.date.available | 2019-10-10T19:28:01Z | en |
| dc.date.issued | 1965 | en |
| dc.description.abstract | Topological groupoids with"approximate" inverses are studied. In the compact case, these"approximate" inverses turn out to be true inverses. Examples of groupoids wL:h"approximate" inverses are given in the section dealing with function spaces. Using the classical construction of Haar as a guide, we succeed in obtaining a (non-trivial) regular, right-invariant measure over a locally compact left group satisfying the conditions: a) open sets are preserved by left translation b) each group component is open. In the section dealing with integrals, we consider a compact metric topological semigroup that is right simple 3nd possesses a right contractive metric (ρ(xz,yz) ≤ ρ(x,y)). It is shown that such a structure always carries a non-trivial right-invariant integral. Throughout the entire development, associativity is invoked only once. The investigation concludes with a section dealing with sufficient conditions under which binary-topological systems become topological groups. A mob-group is defined to be a T<sub>o</sub>-space which is also an algebraic group. A theorem in the last section states that a mob-group is a topological group iff given any open set W about the identity, W ∩ W⁻¹ has non-void interior. | en |
| dc.description.degree | Ph. D. | en |
| dc.format.extent | 109 leaves | en |
| dc.format.mimetype | application/pdf | en |
| dc.identifier.uri | http://hdl.handle.net/10919/94545 | en |
| dc.language.iso | en_US | en |
| dc.publisher | Virginia Polytechnic Institute | en |
| dc.relation.isformatof | OCLC# 9304422 | en |
| dc.rights | In Copyright | en |
| dc.rights.uri | http://rightsstatements.org/vocab/InC/1.0/ | en |
| dc.subject.lcc | LD5655.V856 1965.C438 | en |
| dc.subject.lcsh | Topology | en |
| dc.subject.lcsh | Group theory | en |
| dc.title | On mobs with certain group-like properties | en |
| dc.type | Dissertation | en |
| dc.type.dcmitype | Text | en |
| thesis.degree.discipline | Mathematics | en |
| thesis.degree.grantor | Virginia Polytechnic Institute | en |
| thesis.degree.level | doctoral | en |
| thesis.degree.name | Ph. D. | en |
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