Some Wallman compactifications determined by retracts

Author:
H. L. Bentley

Journal:
Proc. Amer. Math. Soc. **33** (1972), 587-593

MSC:
Primary 54D35; Secondary 54C15

MathSciNet review:
0293588

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let *Y* be a Hausdorff compactification of a locally compact space *X* and let be the remainder. Suppose that *K* is a regular Wallman space (i.e. *K* has a base for closed sets which is a ring and which consists of sets each of which is the closure of its interior) and suppose that *K* is a neighborhood retract of *Y*. Under these assumptions, it is proved below that *Y* is a Wallman compactification of *X*.

**[1]**R. A. Aló and H. L. Shapiro,*A note on compactifications and semi-normal spaces*, J. Austral. Math. Soc.**8**(1968), 102–108. MR**0227943****[2]**H. L. Bentley,*Some Wallman compactifications of locally compact spaces*, Fund. Math.**75**(1972), no. 1, 13–24. MR**0305349****[3]**E. S. Berney,*On Wallman compactifications*, Notices Amer. Math. Soc.**17**(1970), 215. Abstract #672-464.**[4]**C. M. Biles,*Wallman-type compactifications*(unpublished notes).**[5]**Karol Borsuk,*Theory of retracts*, Monografie Matematyczne, Tom 44, Państwowe Wydawnictwo Naukowe, Warsaw, 1967. MR**0216473****[6]**Orrin Frink,*Compactifications and semi-normal spaces*, Amer. J. Math.**86**(1964), 602–607. MR**0166755****[7]**John G. Hocking and Gail S. Young,*Topology*, Addison-Wesley Publishing Co., Inc., Reading, Mass.-London, 1961. MR**0125557****[8]**J. W. Rogers Jr.,*On compactifications with continua as remainders*, Fund. Math.**70**(1971), no. 1, 7–11. MR**0283763****[9]**A. K. Steiner and E. F. Steiner,*Compactifications as closures of graphs*, Fund. Math.**63**(1968), 221–223. MR**0238270****[10]**A. K. Steiner and E. F. Steiner,*Products of compact metric spaces are regular Wallman*, Nederl. Akad. Wetensch. Proc. Ser. A 71 = Indag. Math.**30**(1968), 428–430. MR**0247603****[11]**A. K. Steiner and E. F. Steiner,*Wallman and 𝑍-compactifications*, Duke Math. J.**35**(1968), 269–275. MR**0227942****[12]**E. F. Steiner,*Wallman spaces and compactifications*, Fund. Math.**61**(1967/1968), 295–304. MR**0222849**

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC:
54D35,
54C15

Retrieve articles in all journals with MSC: 54D35, 54C15

Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1972-0293588-8

Keywords:
Wallman compactification,
normal base,
locally compact space,
retract

Article copyright:
© Copyright 1972
American Mathematical Society