View source for Freudenthal compactification

A maximal compactification with zero-dimensional remainder (cf. [[Remainder of a space|Remainder of a space]]). Every [[Peripherically-compact space|peripherically-compact space]] has a Freudenthal compactification (this was proved by H. Freudenthal ). Among all such extensions there is a unique maximal one, and it is called the Freudenthal compactification (sometimes a Freudenthal compactification just means any compactification with zero-dimensional remainder). The Freudenthal compactification can be characterized as the (unique) perfect compactification with zero-dimensional remainder, and also as the minimal perfect compactification (see ).

====References====
<table><TR><TD valign="top">[1a]</TD> <TD valign="top">  H. Freudenthal,   "Neuaufbau der Endentheorie"  ''Ann. of Math.'' , '''43''' :  2  (1942)  pp. 261–279</TD></TR><TR><TD valign="top">[1b]</TD> <TD valign="top">  H. Freudenthal,   "Kompaktisierungen und Bikompaktisierungen"  ''Indag. Math.'' , '''13'''  (1951)  pp. 184–192</TD></TR><TR><TD valign="top">[2]</TD> <TD valign="top">  E.G. Sklyarenko,   "Bicompact extensions of semibicompact spaces"  ''Dokl. Akad. Nauk SSSR'' , '''120''' :  6  (1958)  pp. 1200–1203  (In Russian)</TD></TR><TR><TD valign="top">[3a]</TD> <TD valign="top">  E.G. Sklyarenko,   "Some questions in the theory of bicompactifications"  ''Izv. Akad. Nauk SSSR Ser. Mat.'' , '''26''' :  3  (1962)  pp. 427–452  (In Russian)</TD></TR><TR><TD valign="top">[3b]</TD> <TD valign="top">  E.G. Sklyarenko,   "Bicompactifications with punctiform boundary and their cohomology groups"  ''Izv. Akad. Nauk SSSR Ser. Mat.'' , '''27''' :  5  (1963)  pp. 1165–1180  (In Russian)</TD></TR></table>



====Comments====
See also [[Compact extension|Compact extension]]; [[Compactification|Compactification]].

The Freudenthal compactification is used in the theory of topological groups (cf. [[Topological group|Topological group]]).