Selection principles in hyperspaces

• Ano de defesa: 2018
• Autor(a) principal: Mezabarba, Renan Maneli
• Tipo de documento: Tese
• Tipo de acesso: Acesso aberto
• Idioma: eng
• Instituição de defesa: Biblioteca Digitais de Teses e Dissertações da USP
• Palavras-chave em Português: Espaços de funções; Function spaces; Hiperespaços; Hyperspaces; Jogos topológicos; Princípios seletivos; Selection principles; Topological games
• Link de acesso: http://www.teses.usp.br/teses/disponiveis/55/55135/tde-10102018-144937/

In this work we analyze some selection principles over some classes of hyperspaces. In the first part we consider selective variations of tightness over a class of function spaces whose topologies are determined by bornologies on the space. As results, we extend several well known translations between covering properties and closure properties of the topology of pointwise convergence. In the second part we consider artificial hyperspaces that assist the analysis of productive topological properties. We emphasize the results characterizing productively ccc preorders and the characterization of the Lindelöf property via closed projections.