This paper introduces three separation conditions for topological spaces, called T0,1, T0,2 ("pre-Hausdorff"), and T1,2. These conditions generalize the classical T1 and T 2 separation axioms, and they have advantages over them topologically which we discuss. We establish several different characterizations of pre-Hausdorff spaces, and a characterization of Hausdorff spaces in terms of pre-Hausdorff. We also discuss some classical Theorems of general topology which can or cannot be generalized by replacing the Hausdorff condition by pre-Hausdorff.
In this paper we use initial hulls to define zero dimensional (and other) objects in topological categories. In the process we characterize some initial hulls in the category of topological spaces. Examples of zero dimensional objects in several topological categories are given. We relate zero dimensional objects to preT 2 objects via a Theorem which generalizes their relationship for topological spaces.
The purpose of this study was to determine if recommendations made as a result of the administration of the Cougar Home Safety Assessment Version 4.0 (CHSA 4.0) were effective in causing older residents to make environmental safety modifications in their homes. Initial data were collected during the administration of the CHSA 4.0 in the homes of 40 older people in four northeastern states. After completing the initial assessments, the researchers provided the participants with recommendations for improving the environmental safety of their homes. Approximately one month later, each home was reassessed with the CHSA 4.0. Overall, improvement in environmental safety was demonstrated in the homes with the greatest increases being in fire safety, emergency phone number placement, and bathroom safety. A t-test demonstrated a significant gain in compliance (t = 7.8, p < .001) by comparing the difference between the mean initial and reassessment home safety scores. A very large effect size (Cohen’s d = 1.7) was also found, indicating a high magnitude of difference between initial and reassessment safety ratings. The assessment proved to be beneficial in increasing the environmental safety of homes.
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