| Abstract: | Abstract The relationship between Wallman's construction of a compact T1-space 9] and Flachsmeyer's inverse limit spaces of inverse systems of decomposition spaces 2] is investigated. There are connections between Wallman spaces and inverse limits, which were initiated by Alexandroff in 1928. Some old theorems using inverse limits have shorter proofs now. On the other hand we obtain a new method to treat Wallman compactifications in terms of inverse limit spaces. A suitable notion in this context is the “prime-filter space”, having an interesting maximality property. This space seems to be proper to examine prime ideals in C(X). |
