Banca de DEFESA: ENATHIELLE THIALA SOUZA DE ANDRADE

Uma banca de DEFESA de MESTRADO foi cadastrada pelo programa.
DISCENTE : ENATHIELLE THIALA SOUZA DE ANDRADE
DATA : 03/05/2019
HORA: 15:00
LOCAL: Sala 12 da Pós-Graduacao do IME/UFBA
TÍTULO:

Selection Principles, Topological Games, Star Covering Properties and Generalizations

PALAVRAS-CHAVES:

selection principles; topological games; Rothberger, Menger and Hurewicz spaces; star covering properties; star selection principles.

PÁGINAS: 115
GRANDE ÁREA: Ciências Exatas e da Terra
ÁREA: Matemática
SUBÁREA: Álgebra
ESPECIALIDADE: Lógica Matemática
RESUMO:

This paper addresses the best known selection principles and uses the topological games associated with them to study results that involve the topological spaces that satisfy these principles. For example, we will show that if $ X $ is a Lindelöf space such that $ | X | <$ cov ($ \ mathcal {M} $), then player $ ONE $ has no winning strategy for $ G_1 (\ mathcal {O} _X, \ mathcal {O} _X) $ '', and this proves that `` Every Lindelöf space with a cardinality smaller than cov $ (\ mathcal {M}) $ is a Rothberger space ' '. In this dissertation we will also study $ D $ - spaces, selectively c.c.c. and star selection principles. We present proofs for relevant results of the literatura, such as ``Every  $T_1$ Menger space is a $ D-space '', which is demonstrated via games (using another result whose proof is presented in detail in the dissertation, which is " $ X $ is a Menger space if, and only if, $ ONE $ does not have a winning strategy for $ G \ textrm {fin}} (\ mathcal {O} _X, \ mathcal {O} _X $ '').  As $T_1$  Menger spaces  are D-spaces, one concludes that a counterexample to the conjecture `` All Lindelöf space and regular is a D-space? '', which remains unanswered since the 1970?s, can not be a Menger space.

MEMBROS DA BANCA:
Presidente - 1522833 - SAMUEL GOMES DA SILVA
Externo à Instituição - RODRIGO ROQUE DIAS
Externo à Instituição - VLADIMIR PESTOV