Regarding the terminology "regular" suggested by Myles, I had written "a CW complex structure is said to be regular if each of its attaching maps is a homeomorphism" but of course I meant "homeomorphism onto its image". Apologies for the confusion. Todd ----- Original Message ----- From: "Prof. Peter Johnstone" <P.T.Johnstone@dpmms.cam.ac.uk> To: "Richard Garner" <richard.garner@mq.edu.au> Sent: Wednesday, October 20, 2010 6:50 AM Subject: categories: Re: terminology for simplicial sets
Dear Richard,
Yes, that is relevant. But I don't think one can really use "semi-simplicial" as an adjective to qualify "simplicial set"; and I don't want to call them "semi-simplicial sets" since I want to think of them as simplicial sets with an additional property.
I hesitate before adding one more mathematical usage of the word "regular"; but Myles Tierney informs me that it does at least have a respectable pedigree in this context (it was used by Steenrod), and it's surely better than Peter May's "Property A".
Peter
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