Similarity and Difference between Separable Space and Separated space?
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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 yesterday
Asaf Karagila♦
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up vote
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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 yesterday
Asaf Karagila♦
299k32420750
asked yesterday
High GPA
862419
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
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 yesterday
Asaf Karagila♦
299k32420750
asked yesterday
High GPA
862419
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 yesterday
Asaf Karagila♦
299k32420750
asked yesterday
High GPA
862419
edited yesterday
Asaf Karagila♦
299k32420750
asked yesterday
High GPA
862419
edited yesterday
Asaf Karagila♦
299k32420750
edited yesterday
Asaf Karagila♦
299k32420750
edited yesterday
Asaf Karagila♦
299k32420750
299k32420750
asked yesterday
High GPA
862419
asked yesterday
High GPA
862419
asked yesterday
High GPA
862419
862419
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 yesterday
mathworker21
7,9831827
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
1
down vote
No. Consider $X = {a,b}$ just two elements and $mathcal{T} = {emptyset, X}$. This is separable, second countable, and not even $T_0$.
answered yesterday
mathworker21
7,9831827
add a comment |
up vote
1
down vote
No. Consider $X = {a,b}$ just two elements and $mathcal{T} = {emptyset, X}$. This is separable, second countable, and not even $T_0$.
answered yesterday
mathworker21
7,9831827
add a comment |
up vote
1
down vote
up vote
1
down vote
No. Consider $X = {a,b}$ just two elements and $mathcal{T} = {emptyset, X}$. This is separable, second countable, and not even $T_0$.
answered yesterday
mathworker21
7,9831827
No. Consider $X = {a,b}$ just two elements and $mathcal{T} = {emptyset, X}$. This is separable, second countable, and not even $T_0$.
answered yesterday
mathworker21
7,9831827
answered yesterday
mathworker21
7,9831827
answered yesterday
mathworker21
7,9831827
answered yesterday
mathworker21
7,9831827
7,9831827
add a comment |
add a comment |
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