discrete topology - 2023 Penn Bowl (Harvard)

Question

The metric that is equal to 1 if x is not equal to y, and equal to 0 if x is equal to y induces this topology. For 10 points each:

[10h] Identify this finest possible topology in which all subsets are open.

ANSWER: discrete topology

[10e] Any function from the discrete topology to another topological space always has this property because the pullback is always open. Functions with this property can be sketched without lifting the pencil from the paper.

ANSWER: continuity [or continuous functions]

[10m] The discrete topology has this property if it is finite. Topological spaces have this property if every open cover contains a finite subcover.

ANSWER: compactness

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Summary


2023 Penn Bowl @ Waterloo	10/28/2023	Y	4	27.50	100%	100%	75%
2023 Penn Bowl @ FSU	10/28/2023	Y	2	15.00	100%	50%	0%
2023 Penn Bowl (Harvard)	10/21/2023	Y	3	20.00	100%	67%	33%
2023 Penn Bowl (Mainsite)	10/21/2023	Y	6	21.67	100%	67%	50%
2023 Penn Bowl (Norcal)	10/28/2023	Y	2	20.00	100%	100%	0%
2023 Penn Bowl (South Central)	10/28/2023	Y	3	20.00	100%	67%	33%
2023 Penn Bowl (UK)	10/28/2023	Y	5	24.00	100%	100%	40%
2023 Penn Bowl @ UNC	10/28/2023	Y	4	22.50	100%	75%	50%

Data


MIT	Brandeis	10	10	10	30
Brown	Boston College	0	10	0	10
Harvard	Tufts	0	10	10	20