- #1
jeff1evesque
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I am reading from my text, and was just wondering if someone could provide additional information on the following examples.
0.1 Examples. For any set X each of the following defines a topology for X.
(1) [tex]T_{*} = {A \subseteq X|a \in A \Rightarrow X \subseteq A},[/tex] Indiscrete Topology.
(2) [tex]T^{*} = {A \subseteq X|a \in A \Rightarrow {a} \subseteq A},[/tex] Discrete Topology.
Questions:
I was wondering how we can have the following statement (from above),
(1) [tex]a \in A \Rightarrow X \subseteq A[/tex]
(2) [tex]a \in A \Rightarrow {a} \subseteq A[/tex]
Thanks,JL
0.1 Examples. For any set X each of the following defines a topology for X.
(1) [tex]T_{*} = {A \subseteq X|a \in A \Rightarrow X \subseteq A},[/tex] Indiscrete Topology.
(2) [tex]T^{*} = {A \subseteq X|a \in A \Rightarrow {a} \subseteq A},[/tex] Discrete Topology.
Questions:
I was wondering how we can have the following statement (from above),
(1) [tex]a \in A \Rightarrow X \subseteq A[/tex]
(2) [tex]a \in A \Rightarrow {a} \subseteq A[/tex]
Thanks,JL