Parody is easy....topology is hard!
In this short story, I made use of (and made fun of) the classic superhero comic book genre to illustrate some ideas from topology. So, we end up seeing a battle between Topology Man (who can change the topology of objects) and his archenemy Homotopy (with the power to change objects in ways that preserve their topology).
Contributed by
Mark Nelson
I recently read your collection of mathematical fiction
"Reality Conditions". Whilst there were several stories that were
particularly good, one stood out for me: The Adventures of Topology
Man. Not because I am a topologist nor because I know what category
theory is. But I just loved the superhero dialogue
"Only a functor of evil, Homotopy!"
It cracked me up.
I'm looking forward to reading more Topology Man in your next
collection!

My next collection? Now, you're cracking me up!
Anyway, this story was not meant to be taken too seriously, but still to give some sense of what orientability is, what it means for a space to be Hausdorff, etc.
Perhaps reviewer Mary Gray (Mathematical Intelligencer) took it a bit too seriously when she expressed concern about the name of another superhero in the story: Category Theory Girl. Yes, I was perfectly aware of the fact that calling the male character "man" and the female character "girl" was inequitable. But, this is of course the way it was done in the classic comic books, and I was just turning it into a joke. (You will note that Category Theory Girl is both more powerful as a hero and also a better mathematician than the title character!)
Contributed by
Mark Nelson
Yes, I liked "Topology Man"... but I have received a heavy dosage
of "superhero comics" and I enjoyed the way that you sent up the genre.
Reading through your email it occurred to me that "Topology Man"
was different to the other stories, in that it offered an intriguing
teaching idea. Now, I will never ever in my life teach a course in
topology. But if I did... it would be interesting to give the students
a copy of "Topology Man" at the start of the course. Then at
appropriate times within the course refer back to the story to show
how it illustrates the theorems. Then in the final
assignment it might be fun to say "How could Topology Man use the
following theorems to help fight crime?". With the right students
you might even give them, as an assignment, the task of writing a new
chapter in the life of "Topology Man". And once I am thinking along
these lines, perhaps there are other mathematical superheroes writing
to be discovered...

Contributed by
LiChung Hung
"The Adventures of Topology Man" is very interesting. When the definition of Hausdorff is mentioned in this story, the scene is quite funny and made a deep impression on me. LiChung

Contributed by
Kevin Roberge
I'd love it if someone illustrated this! As with many of the stories in Reality Conditions this one is great. It takes mathematics we have all seen in the classroom and made jokes about in the office and weaves a story about it. I also liked the way it fit into the superhero genre. I'm a little new to that genre but have been working my way into it. I suppose another reason I'm partial to this story is that I'm studying algebraic topology myself and have always enjoyed the area. Anyways, funny story, great lines and a great way to illustrate how important it is for our space to be Hausdorff.

Contributed by
Andrew Breslin
As a previous commenter observed, "only a functor of evil, Homotopy!" had me laughing out loud. And mind you, I find the shorthand "lol!" to be obnoxious in the extreme as it is untrue 99% of the time it is used. But I truly did laugh out loud.
"What's so funny?" the people on the subway asked.
"Topology."
"What's that?"
"The study of the properties of geometric figures or solids that are not changed by bicontinuous onetoone transformations," I replied.
They let me return to my reading. Some of them moved to more distant seats.

New for April 1st 2016: You asked for it. (Well, some people asked for it...maybe not you personally.) Now, finally, here it is. The cover of the longawaited comic book version of this mathematical comic book parody has been "leaked to the press" prior to its official publication. (Rumor has it that the international hackster known by the codename "Hauke" is responsible for the leak.) Click on the image to see it fullsized:
