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As pointed out in comments, the first part is answered here: A space in which sequences have unique limits but compact sets need not be closedA space in which sequences have unique limits but compact sets need not be closed.

The second question is answered on math.SE in the question Cartesian product of KC spaces.

I am posting this CW answer, so that this question does not remain unanswered

As pointed out in comments, the first part is answered here: A space in which sequences have unique limits but compact sets need not be closed.

The second question is answered on math.SE in the question Cartesian product of KC spaces.

I am posting this CW answer, so that this question does not remain unanswered

As pointed out in comments, the first part is answered here: A space in which sequences have unique limits but compact sets need not be closed.

The second question is answered on math.SE in the question Cartesian product of KC spaces.

I am posting this CW answer, so that this question does not remain unanswered

replaced http://math.stackexchange.com/ with https://math.stackexchange.com/
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As pointed out in comments, the first part is answered here: A space in which sequences have unique limits but compact sets need not be closed.

The second question is answered on math.SE in the question Cartesian product of KC spacesCartesian product of KC spaces.

I am posting this CW answer, so that this question does not remain unanswered

As pointed out in comments, the first part is answered here: A space in which sequences have unique limits but compact sets need not be closed.

The second question is answered on math.SE in the question Cartesian product of KC spaces.

I am posting this CW answer, so that this question does not remain unanswered

As pointed out in comments, the first part is answered here: A space in which sequences have unique limits but compact sets need not be closed.

The second question is answered on math.SE in the question Cartesian product of KC spaces.

I am posting this CW answer, so that this question does not remain unanswered

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Martin Sleziak
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As pointed out in comments, the first part is answered here: A space in which sequences have unique limits but compact sets need not be closed.

The second question is answered on math.SE in the question Cartesian product of KC spaces.

I am posting this CW answer, so that this question does not remain unanswered

Post Made Community Wiki by Martin Sleziak