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Similarity and Difference between Separable Space and Separated space?
Does separability and/or second countability implies $T_2$ or higher axiom sets?
My intuition is "no". Even $T_0$ space can be separability and/or second countability?
general-topology separation-axioms separable-spaces second-countable
edited Nov 20 '18 at 23:43
Asaf Karagila♦
302k32426756
asked Nov 20 '18 at 22:17
High GPA
889419
add a comment |
Does separability and/or second countability implies $T_2$ or higher axiom sets?
My intuition is "no". Even $T_0$ space can be separability and/or second countability?
general-topology separation-axioms separable-spaces second-countable
edited Nov 20 '18 at 23:43
Asaf Karagila♦
302k32426756
asked Nov 20 '18 at 22:17
High GPA
889419
add a comment |
Does separability and/or second countability implies $T_2$ or higher axiom sets?
My intuition is "no". Even $T_0$ space can be separability and/or second countability?
general-topology separation-axioms separable-spaces second-countable
edited Nov 20 '18 at 23:43
Asaf Karagila♦
302k32426756
asked Nov 20 '18 at 22:17
High GPA
889419
Does separability and/or second countability implies $T_2$ or higher axiom sets?
My intuition is "no". Even $T_0$ space can be separability and/or second countability?
general-topology separation-axioms separable-spaces second-countable
general-topology separation-axioms separable-spaces second-countable
edited Nov 20 '18 at 23:43
Asaf Karagila♦
302k32426756
asked Nov 20 '18 at 22:17
High GPA
889419
edited Nov 20 '18 at 23:43
Asaf Karagila♦
302k32426756
asked Nov 20 '18 at 22:17
High GPA
889419
edited Nov 20 '18 at 23:43
Asaf Karagila♦
302k32426756
edited Nov 20 '18 at 23:43
Asaf Karagila♦
302k32426756
edited Nov 20 '18 at 23:43
Asaf Karagila♦
302k32426756
302k32426756
asked Nov 20 '18 at 22:17
High GPA
889419
asked Nov 20 '18 at 22:17
High GPA
889419
asked Nov 20 '18 at 22:17
High GPA
889419
889419
add a comment |
add a comment |
1 Answer
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No. Consider $X = {a,b}$ just two elements and $mathcal{T} = {emptyset, X}$. This is separable, second countable, and not even $T_0$.
answered Nov 20 '18 at 22:25
mathworker21
8,6521928
add a comment |
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No. Consider $X = {a,b}$ just two elements and $mathcal{T} = {emptyset, X}$. This is separable, second countable, and not even $T_0$.
answered Nov 20 '18 at 22:25
mathworker21
8,6521928
add a comment |
No. Consider $X = {a,b}$ just two elements and $mathcal{T} = {emptyset, X}$. This is separable, second countable, and not even $T_0$.
answered Nov 20 '18 at 22:25
mathworker21
8,6521928
add a comment |
No. Consider $X = {a,b}$ just two elements and $mathcal{T} = {emptyset, X}$. This is separable, second countable, and not even $T_0$.
answered Nov 20 '18 at 22:25
mathworker21
8,6521928
No. Consider $X = {a,b}$ just two elements and $mathcal{T} = {emptyset, X}$. This is separable, second countable, and not even $T_0$.
answered Nov 20 '18 at 22:25
mathworker21
8,6521928
answered Nov 20 '18 at 22:25
mathworker21
8,6521928
answered Nov 20 '18 at 22:25
mathworker21
8,6521928
answered Nov 20 '18 at 22:25
mathworker21
8,6521928
8,6521928
add a comment |
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