16,837 research outputs found

    A new look at Counterexamples in topology

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    The book Counterexamples in Topology is a useful catalogue of topological spaces and properties. This thesis extends that catalogue to the properties of sobriety and packedness, and describes some related theory. A purely topological account of sobriety and sober reflections is given, together with an account of the connection with point-free topology which motivates it. Concrete constructions of the sober, T0 and T1 reflections of a topological space are given, and these are calculated for each space in Counterexamples in Topology. These are used to study the relationship between sobriety and the T1 separation property. The notion of a specialization topology is introduced as a means of constructing topological spaces from quasiordered sets. The Alexandrov, Scott and weak topologies are described and shown to be examples of this notion. The sobriety and sober reflections of specialization topologies are considered, and these motivate a suggestion for a generalization of the notion of a topological space. The calculations in this thesis are summarized in two reference tables

    The Uniform Schanuel Conjecture Over the Real Numbers

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    We prove that Schanuel's conjecture for the reals is equivalent to a uniform version of itself

    Study of passenger subjective response to ideal and real-vehicle vibration environments

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    The stimulus received by subjects tested on the passenger ride quality apparatus (PRQA) is defined. Additional analyses on the data collected from field tests using buses, were conducted to assess the relation between subjective ratings of ride quality and vibrations measured on the buses, and to better define the vibration stimulus measured in the field. The relation of subjective evaluation of simulations of bus rides produced by the DRQA to subjective evaluations of the actual bus rides is discussed. The relative contribution of the seat and floor vibration to human comfort in a simulated aircraft ride environment is discussed along with the determination of equal comfort curves through magnitude estimation