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. / Ph. D.
| Identifer | oai:union.ndltd.org:VTETD/oai:vtechworks.lib.vt.edu:10919/94545 |
| Date | January 1965 |
| Creators | Chew, James Francis |
| Contributors | Mathematics |
| Publisher | Virginia Polytechnic Institute |
| Source Sets | Virginia Tech Theses and Dissertation |
| Language | en_US |
| Detected Language | English |
| Type | Dissertation, Text |
| Format | 109 leaves, application/pdf, application/pdf |
| Rights | In Copyright, http://rightsstatements.org/vocab/InC/1.0/ |
| Relation | OCLC# 9304422 |
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