Thesis (doctoral)--Rheinische Friedrich-Wilhelms-Universität Bonn, 2000. / Includes bibliographical references (p. 99-102) and index.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1975. / Typpescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.

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O problema de Scarborough-Stone consiste em perguntar se o produto de espaços topológicos sequencialmente compactos precisa ser enumeravelmente compacto. Nesse trabalho estudamos alguns resultados que surgiram tentando resolver tal problema. Começamos com uma resposta negativa em ZFC usando espaços T2 e depois especificamos melhor condições sobre os axiomas de separação envolvendo os espaços do produto. Veremos respostas positivas envolvendo alguns axiomas de separação mais fortes como T6 (usando MA e a negação de CH) e T5 (usando o PFA). Além disso construímos mais respostas negativas usando construções como a Reta de Ostaszewski, espaços de Franklin-Rajagopalan e estruturas envolvendo álgebras Booleanas. / The Scarborough-Stone problem asks if every product of sequentially compact spaces must be a countably compact space. In this work we study some results that have arisen in attempt to solve this problem. We start our results with a negative answer in ZFC using T2 spaces and specify our conditions about the separability axioms of the spaces of the product. We will see positive answers assuming stronger separability axioms like T6 (using MA and the negation of CH) and T5 (using the PFA). We also construct more negative answers using constructions like the Ostaszewski line, Franklin-Rajagopalan spaces and structures involving Boolean algebras.

Neste trabalho investigamos problemas sobre reflexão de funções cardinais, fazendo uso de técnicas como submodelos elementares e Teoria PCF. Mostramos que o grau de Lindelöf reflete todos os cardinais fortemente inacessíveis e que um exemplo de espaço onde a mesma função cardinal não reflita um cardinal fracamente inacessível requer a existência de 0#. Além disso, estendemos um resultado de reflexão do caráter, de espaços Lindelöf para espaços linearmente Lindelöf, obtendo novas equivalências com a Hipótese do Contínuo (CH). Obtivemos ainda várias respostas parciais para problemas clássicos deste tópico de pesquisa. / This work investigates problems about reflection of cardinal functions, using techniques such as elementary submodels and PCF Theory. We show that the Lindelöf degree reflects all the strongly inaccessible cardinals and that a example of a space in which the same cardinal function does not reflect a weakly inaccessible cardinal requires \"0# exists\". Furthermore, we extend a result of reflection of the character from Lindelöf spaces to linearly Lindelöf spaces, obtaining new equivalences with the Continuum Hypothesis (CH). We also obtained several partial answers to classic problems of this research topic.

Neste trabalho investigamos problemas sobre reflexão de funções cardinais, fazendo uso de técnicas como submodelos elementares e Teoria PCF. Mostramos que o grau de Lindelöf reflete todos os cardinais fortemente inacessíveis e que um exemplo de espaço onde a mesma função cardinal não reflita um cardinal fracamente inacessível requer a existência de 0#. Além disso, estendemos um resultado de reflexão do caráter, de espaços Lindelöf para espaços linearmente Lindelöf, obtendo novas equivalências com a Hipótese do Contínuo (CH). Obtivemos ainda várias respostas parciais para problemas clássicos deste tópico de pesquisa. / This work investigates problems about reflection of cardinal functions, using techniques such as elementary submodels and PCF Theory. We show that the Lindelöf degree reflects all the strongly inaccessible cardinals and that a example of a space in which the same cardinal function does not reflect a weakly inaccessible cardinal requires \"0# exists\". Furthermore, we extend a result of reflection of the character from Lindelöf spaces to linearly Lindelöf spaces, obtaining new equivalences with the Continuum Hypothesis (CH). We also obtained several partial answers to classic problems of this research topic.

We aim to explain the intuition behind several large cardinal axioms, give characterization theorems for these axioms, and then discuss a few of their properties. As a capstone, we hope to introduce a new large cardinal notion and give a similar characterization theorem of this new notion. Our new notion of near strong compactness was inspired by the similar notion of near supercompactness, due to Jason Schanker.

O problema de Scarborough-Stone consiste em perguntar se o produto de espaços topológicos sequencialmente compactos precisa ser enumeravelmente compacto. Nesse trabalho estudamos alguns resultados que surgiram tentando resolver tal problema. Começamos com uma resposta negativa em ZFC usando espaços T2 e depois especificamos melhor condições sobre os axiomas de separação envolvendo os espaços do produto. Veremos respostas positivas envolvendo alguns axiomas de separação mais fortes como T6 (usando MA e a negação de CH) e T5 (usando o PFA). Além disso construímos mais respostas negativas usando construções como a Reta de Ostaszewski, espaços de Franklin-Rajagopalan e estruturas envolvendo álgebras Booleanas. / The Scarborough-Stone problem asks if every product of sequentially compact spaces must be a countably compact space. In this work we study some results that have arisen in attempt to solve this problem. We start our results with a negative answer in ZFC using T2 spaces and specify our conditions about the separability axioms of the spaces of the product. We will see positive answers assuming stronger separability axioms like T6 (using MA and the negation of CH) and T5 (using the PFA). We also construct more negative answers using constructions like the Ostaszewski line, Franklin-Rajagopalan spaces and structures involving Boolean algebras.

This study is a psychobiographical study, aiming to explore and describe the life of John Henry Newman (1801-1890), a theologian, priest, and cardinal of the Roman Catholic Church, through the application of Erik Erikson’s theory of Psychosocial Development. Newman is a significant figure in the English-speaking Christian world and his life and thought remains of interest and importance, particularly in the fields of philosophy, theology, ecclesiology and education. Newman was beatified in 2010 and therefore this study also considers the hagiographical nature of biographical data. This study utilises a qualitative single case study approach and the subject was selected through purposive sampling based on interest value. Data were collected from primary and secondary sources to enhance validity. The data were analysed by organising and reducing information obtained regarding Newman’s life and then displaying it for discussion. The study considers Newman’s life, reconstructed from birth, through adolescence and adulthood to his death and also considers his posthumous legacy. The main themes of discussion revolve around Newman’s development of his religious identity and his life as a churchman and an academic. It considers how a psychosocially functional individual such as Newman manifests certain dystonic, maladaptive or malignant tendencies such as doubt, shame, guilt and overextension, and how these impact the formation of religious identity and the experience of God and the spiritual life. Basic trust, celibate intimacy and generativity emerged as three significant areas of importance in the Newman’s life and identity. The study highlighted the value of psychobiographical studies and of Erikson’s theory in understanding development. Recommendations for future research in this field are made in the hope of further uncovering and understanding personality, religious identity and psychosocial development.

Este trabalho tem como objetivo apresentar uma coletânea de resultados sobre produtos caixa de espaços topológicos. Com o intuito de comparação com o produto de Tychonoff, apresentamos propriedades do produto caixa relacionadas a espaços discretamente gerados e ao espaço C(X). Em seguida apresentamos alguns resultados relativos ao problema da paracompacidade de produtos caixa, o qual é a principal questão envolvendo este tipo de pro- duto. Por fim, utilizamos o produto caixa para construir dois exemplos de espaços normais cujos produtos não são normais. / The aim of this work is to present a selection of results about box products of topological spaces. In order to compare this product with the Tychonoff product, we present properties of the box products related to discretely generated spaces and to the space C(X). Then we present results on the problem of paracompactness of the box products, wich is the main question regarding this kind of product. At last, we use the box products to create examples of normal spaces whose products are not normal.