A Study Of Spaces Which Are Dually Discrete

D-spaces,being an important part of modern topology,have developed greatly in recent decades.Many famous topologists have done much work on it.In 2007,the idea of D-spaces was then further developed.The concept of dual properties was introduced by J.van Mill,V.V.Tkachuk and R.G.Wislon in 2007.This thesis addresses the properties of dual discrete spaces.The following results on dual discrete spaces are ontained:A F_σsubspace of a dual discrete space is dually discrete,and perfect inverse images of a dual discrete spaces are dually diacrete;IfⅩhas a countable cover of closed dual discrete subspaces,thenⅩis dually discrete;IfⅩis a(dually discrete)—like space,thenⅩis dually discrete;IfⅩhas a closure-preserving cover of closed dual discrete subspaces,thenⅩis dually diasrete; A sufficient condition of dually discrete spaces by definingφsticky sets is given;Some relation between dually discrete spaces and Lindelof spaces are discussed.This thesis is organized as follows.Chapter 1 focuses on some background of D-spaces. Some notations are also introduced,which are needed in the following chapters; In Chapter 2,some properties of dually discrete are derived;In Chapter 3,we discuss some problems on the union of dual discrete spaces;In Chapter 4,a sufficient condition for dual discrete spaces is given;In Chapter 5,we discuss the relation of dual discrete spaces between Lindelof spaces.