This thesis presents a development of some useful concepts concerning topological spaces. Most of the theorems given apply to the most general form of topological space.

The purpose of this thesis is to investigate the idea of topological "connectedness" by presenting some of the basic ideas concerning connectedness along with several related concepts.

In 2018, the Cowichan Therapeutic Riding Association (CTRA) connected with the University of Victoria to initiate a research project focusing on social connectedness. Social connectedness is the psychosocial process of belonging that can be developed within a community context. Feelings of social connectedness can reduce depressive symptoms and suicidal thoughts, lessens violence, health compromising behaviours, and the impact of stress and trauma, and is linked to high self-esteem. The aim of this mixed methods case study was to understand the social connectedness of families participating in a community therapeutic riding program. An explanatory sequential mixed methods design was used to investigate social connectedness at the CTRA. Three different perspectives were sought to explore social connectedness at the CTRA; guardians, children, and instructors. Participants completed the quantitative Connectedness to Treatment Setting Scale (CTSS) in Phase 1, and qualitative semi-structured interviews in Phase 2 to follow-up and expand upon findings from Phase 1. Fifteen participants (guardians (n = 12) and instructors (n = 3)) participated in Phase 1 of the study whereas five guardians (including a guardian and child dyad) and two instructors participated in Phase 2 of the study. The CTSS comprised of 10 questions assessed on a 6-point scale (from 1 = Totally disagree to 6 = Totally agree). Frequencies were computed for each question and overall mean scores (+ SD) were computed for guardians and instructors separately. The interview transcripts were coded twice. Initially, a deductive orientational approach guided by seven attributes of social connectedness was used. Then, an inductive approach was used to examine how social connectedness was experienced, fostered, or hindered at the CTRA, as well as suggestions for improvement. The CTSS scores revealed that the vast majority of guardians and instructors felt highly socially connected at the CTRA. The overall mean score of the guardians was 55.3 (SD = 4.5) and 56.7 (SD = 3.1) among the instructors. All seven attributes of social connectedness were represented in the guardians and instructors’ responses however, trust, caring, and reciprocity were the most evident attributes. Two themes emerged from the inductive analysis: effective communication equates with social connectedness and expectations of services. Guardians reported that communication as a team with their instructor, volunteer(s), and the animals positively influenced their families’ social connectedness. The results suggested that social connectedness might be mediating relationships between negative factors preceding a therapeutic riding session and the experience of that lesson. Although the instructors and majority of families were socially connected at the CTRA, guardians had high expectations of the program and wanted the CTRA to foster connections beyond their son/daughters therapeutic riding lesson by organizing opportunities for peer and family relationships. The people and animals at the CTRA contributed heavily to family’s sense of social connectedness. Most families had a desire to connect and form relationships with the people and animals at the CTRA. The CTRA provides a community context that supports the development of social connectedness. / Graduate

The purpose of this thesis was to explore the potential of a designed physical outdoor environment to improve the social environment and thereby enhance the psychological healing process at Psychiatric institutions. Weskoppies Psychiatric Hospital situated in Pretoria West served as a model for testing the hypothesis. The physical and social environment at Weskoppies was analyzed through observations, interviews and literature research. Findings from analysis and theoretical research regarding the influences that physical and social outdoor environments have on mental health, were synthesized to establish design guidelines. These informed the design decision making process and assisted in the proposal of an outdoor environment with emotional healing potential. An open space framework and catalytic sketch plan was designed to illustrate the application of the design guidelines. The author found that an outdoor environment that encourage independence, purpose, consciousness, rest, connectedness and physical activities have the potential to enhance the psychological healing process. The open space framework and sketch plan proved that these guidelines can be accommodated on different scales. Copyright / Dissertation (ML(Prof))--University of Pretoria, 2009. / Architecture / unrestricted

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Yes / This paper introduces a novel framework of partial connectedness measures to investigate contagion dynamics between different types of oil price shocks and exchange rates. Oil price shocks are persistent net transmitters of shocks within the network. It is found that the oil shock net spillovers made up most of the net connectedness values in most countries during the pre-COVID-19 period. Both oil exporters and oil importers, without any exception, were all net receivers of shocks. However, during the COVID-19 era, there were significant differences within the groups of countries. It is also observed that the oil-risk shock transmits to the other two types of oil shocks in the pre-COVID-19 and during the COVID-19 periods. The results may have potential implications for traders. / David Gabauer would like to acknowledge that this research has been partly funded by BMK, BMDW, Austria and the Province of Upper Austria in the frame of the COMET Programme managed by FFG, Austria. / The full-text of this article will be released for public view at the end of the publisher embargo on 23 Sep 2024.

The creation and use of models is critical not only to the scientific process, but also to life in general. Selected features of a system are abstracted into a model that can then be used to gain knowledge of the workings of the observed system and even anticipate its future behaviour. A key feature of the modelling process is the identification of commonality. This allows previous experience of one model to be used in a new or unfamiliar situation. This recognition of commonality between models allows standards to be formed, especially in areas such as measurement. How everyday physical objects are measured is built on an ingrained acceptance of their underlying commonality. Complex systems, often with their layers of interwoven interactions, are harder to model and, therefore, to measure and predict. Indeed, the inability to compute and model a complex system, except at a localised and temporal level, can be seen as one of its defining attributes. The establishing of commonality between complex systems provides the opportunity to find common metrics. This work looks at two dimensional cellular automata, which are widely used as a simple modelling tool for a variety of systems. This has led to a very diverse range of systems using a common modelling environment based on a lattice of cells. This provides a possible common link between systems using cellular automata that could be exploited to find a common metric that provided information on a diverse range of systems. An enhancement of a categorisation of cellular automata model types used for biological studies is proposed and expanded to include other disciplines. The thesis outlines a new metric, the C-Value, created by the author. This metric, based on the connectedness of the active elements on the cellular automata grid, is then tested with three models built to represent three of the four categories of cellular automata model types. The results show that the new C-Value provides a good indicator of the gathering of active cells on a grid into a single, compact cluster and of indicating, when correlated with the mean density of active cells on the lattice, that their distribution is random. This provides a range to define the disordered and ordered state of a grid. The use of the C-Value in a localised context shows potential for identifying patterns of clusters on the grid.

This Thesis is dedicated to the variance decompositions from the VAR model un- der the Diebold, Yilmaz (2012) methodology combined with the Baruník, Křehlík (2017) method of frequencies that was used to create traditional and directional spillover tables to be compared under different frequencies. Diverse markets vari- ables were used for the analysis during the period 1/6/1999 to 29/6/2018. The S&P 500 Index represented the financial markets, EUR/USD and YEN/USD rep- resented the Forex markets, and eight types of commodities: Crude Oil, Natural Gas, Gasoline, and Propane represented energy commodities and Corn, Coffee, Wheat, and Soybeans represented food commodities. This analysis contribute to understanding of the dynamic frequency connectedness in case of a differentiated system of markets. The main finding was the strongest short-frequency reaction to shocks in case of all variables, which is opposite behavior than usually observed in banking sector frequency dynamics analyses. JEL Classication: F12, F21, F23, H25, H71, H87 Keywords: connectedness, financial market, forex market, commodity market, systemic risk, spillovers, frequency analysis Author's e-mail: 93414233@fsv.cuni.cz Supervisor's e-mail: barunik@fsv.cuni.cz

Connectedness has been identified as a powerful protective factor for adolescents. This study focused on the extent to which secondary students at the American International School of Utah (AISU) report perceptions of connectedness. Specifically, this work focused on school-level factors. It examined the extent to which participation in the school-wide interventions of Crew and Intensives influence perceptions of connectedness among AISU secondary students. Data collected provided insights about perceptions of connectedness within the AISU environment that may be used to inform current practices, identify additional student support needs, and improve future implementations. An Explanatory Sequential research design was used. This method included the use of quantitative measure administered and analyzed first, followed by a qualitative measure used to learn more about the quantitative results. The Hemingway Measure of Adolescent Connectedness Short Form by Michael Karcher served as the quantitative measure for this study. A semistructured interview protocol, created by the researcher, was used as the qualitative instrument. Results indicated that overall, study participants reported high-levels of connectedness on the Hemingway. Analysis of the Hemingway Subscales revealed that the Friends subscale had the highest levels of connectedness, followed by connectedness to Teacher. Connectedness to School was slightly lower than connectedness to Teachers. Connectedness to Peers showed moderate levels of connectedness. To learn more about the results of the quantitative stage of this study, semistructured interviews were conducted and analyzed using traditional deductive coding techniques. Results showed high-levels of connectedness associated with AISU as a school and with participation in Crew. Findings on the questions asking about Intensives showed that students appear to value the unique learning opportunities and ability to choose what they learn, more than they associated Intensives with connectedness.

How are people in a global society reconstructing their sense of place? This key question is addressed in this thesis. Australian society has emerged from the period of industrialisation and entered the period of globalisation, a modern to a postmodern world. Sense of place is a vital source of both individual and cultural identity and security, a point of departure from which we orient ourselves in the world. The use of a place, its terrain (landscape), connectedness to that place and its inherent meaning are identified here as the 4 key elements in the construction of a sense of place. The case study approach adopted in this thesis examines a former industrial site in Pyrmont currently being redeveloped as a waterfront residential community, known as Jacksons Landing. The site is reviewed at the moment in time it transcends the industrial era and enters the global era. The mixture of research methods examining the transition includes observation; key informant interviews; structured interviews; and document analysis. The study document the shift of the site from 'space' to 'place' through personal presence and association. It catches a glimpse of how individual experience of place is formed from a unique moment in space-time, which is interlinked with memories, emotions and identity. The findings indicate that communities of the future, in the era of globalisation, will be markedly different to those of the industrial era. Results suggest lifestyle and economic factors will shape future communities, which have the potential to be gated and homogenous, representing a microcosm of segmentation and secularisation. Security, income and occupation will be increasingly valued, forming the basis of identity and the shaping of place. / Master of Science (Hons)