A simplification of the Eilenberg-Steenrod axioms, 2

✍ Scribed by Volker Thürey

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 410 KB
• Volume: 129
• Category: Article
• ISSN: 0022-4049
• DOI: 10.1016/s0022-4049(97)00065-0

✦ Synopsis

Since the famous book of it is well known that a homology theory on the category of pairs of linite triangulable spaces and continuous maps is determined by four simple axioms.

In 1988 Dawson showed that in the much smaller category of pairs of finite simplicial complexes and simplicial maps one can replace this system of axioms by a simpler one, i.e., by replacing the dimension axiom and omitting the homotopy axiom.

In this paper I will show that it is also possible to do the same on the bigger category which was dealt with by Eilenberg and Steemod. My proof uses ideas of Dawson, but it is easier. The second theorem shows that the homotopy axiom is nearly redundant. @