Editing 2625: Field Topology

{{comic
| number    = 2625
| date      = May 27, 2022
| title     = Field Topology
| image     = field_topology.png
| titletext = The combination croquet set/10-lane pool can also be used for some varieties of foosball and Skee-Ball.
}}

==Explanation==
{{incomplete|Created by SOMEBODY TOPOLOGICALLY EQUIVALENT TO YOU - Please change this comment when editing this page. Do NOT delete this tag too soon.}}

This comic strip depicts a logical extreme of multi-use athletic facilities, in which sports are grouped by the {{w|topology|topological}} equivalence of their fields (not to be confused with {{w|Field (mathematics)|mathematical fields}}, or the {{w|Fields Medal}} prize -- although successfully {{w|Straightedge and compass construction|constructing}} these fields might lead to medals of one kind or another being granted).

In topology, shapes which can be smoothly deformed into one another, without making or closing cuts or holes, are equivalent. {{w|Baseball}}, {{w|soccer}}, and {{w|tetherball}} are played on fields without any holes that the ball or players can completely pass through, so they are grouped ({{w|Group (mathematics)|heh!}}) into one continuous field without holes. The goals on a soccer field do not create holes; because the goalposts are connected to the field with a net, the goals and field are topologically equivalent to a plane. The same is true of ice hockey, as well.

{{w|Volleyball}} and {{w|badminton}} are played on a field split in two by a net, and the {{w|high jump}} has a bar that contestants jump over. The space bounded by the bottom of the net (or bar), the supporting poles, and the ground can be considered to be a hole, so their fields all have one "hole". 

A basketball court has two holes, the nets. Parallel bars can be thought of as two rectangles and thus as two topographical "holes". A football field is a special case. Commonly, an American football field uses a "Y" shaped upright, making the field topologically equivalent to a plane. However, at lower levels of play (primary and secondary schools), sometimes an "H" shaped upright is used, which creates a topological hole under the crossbar at both ends of the field. The comic might instead refer to Gaelic football or Rugby, both of which use "H" shaped goals and are called "football" in certain contexts.

The lane dividers in swimming create bounded holes on the 'playing surface' equivalent to the number of lanes minus one. And each hoop in croquet is a hole with one edge bounded by the playing surface. Similarly, as mentioned in the title text, this configuration is also {{w|homeomorphism|homeomorphic}} to a {{w|foosball}} table (with each rod sustaining the player figures above the table defining a hole) or a {{w|Skee-Ball}} lane (which is even more straightforward, as it is just a plane with several holes in which to throw balls).

==Transcript==
{{incomplete transcript|Do NOT delete this tag too soon.}}

Four indistinct shapes with various numbers of holes in, with signs next to them

zero holes: "Baseball. Soccer. Tetherball."

one hole: "Volleyball. Badminton. High jump."

two holes: Basketball. Football. Parallel bars."

nine holes: "Olympic swimming. Croquet."

Image caption: "No one ever wants to use the topology department's athletic fields."

{{comic discussion}}
[[Category:Math]]
[[Category:Sport]]