| In this thesis,we study the soft connectivity,soft separation and soft compactness of the soft topological spaces,and further discuss the relationship between soft compactness and soft separation in soft topological space.Firstly,combined with soft sets and related concepts,soft isolation sets in soft topological space are defined.By using soft isolation sets,the definition of soft disconnection in soft topological space is given.The properties of soft disconnection in soft topological space are studied.The equivalent characterization of soft disconnection is proved.From the equivalence relation of soft connectivity of soft points,the concept of soft connected branches is given,and equivalence characterization of the soft connected branches is studied.The definition of soft locally connected space is given,and the properties of soft locally connected space are studied.Secondly,combined with the definition and properties of soft separation in soft topological space,the soft separation in soft topological space is further studied,and the equivalent characterization of soft1T-space is obtained.The sufficient and necessary conditions for the establishment of soft complete normal space are obtained.Every soft complete normal space is soft normal space,so it is concluded that soft complete normal space has soft topological invariance.Finally,combined with the definition and properties of soft compactness in soft topological space,the properties of soft compactness in soft topological space are further explored.It is concluded that soft compactness in soft topological space has soft topological invariance,and that any finite soft compact subset is still soft compact.The definition of soft countable compact space is given.The properties of soft countable compact space are discussed.It is concluded that the soft countable compactness of soft topological space has soft topology invariance,and the relationship between compactness and separation in soft topological space is also explored. |
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