# A generalization of Magill's Theorem for non-locally compact spaces

Gary D. Faulkner; Maria Cristina Vipera

Commentationes Mathematicae Universitatis Carolinae (1995)

- Volume: 36, Issue: 1, page 127-136
- ISSN: 0010-2628

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topFaulkner, Gary D., and Vipera, Maria Cristina. "A generalization of Magill's Theorem for non-locally compact spaces." Commentationes Mathematicae Universitatis Carolinae 36.1 (1995): 127-136. <http://eudml.org/doc/247720>.

@article{Faulkner1995,

abstract = {In the theory of compactifications, Magill's theorem that the continuous image of a remainder of a space is again a remainder is one of the most important theorems in the field. It is somewhat unfortunate that the theorem holds only in locally compact spaces. In fact, if all continuous images of a remainder are again remainders, then the space must be locally compact. This paper is a modification of Magill's result to more general spaces. This of course requires restrictions on the nature of the function.},

author = {Faulkner, Gary D., Vipera, Maria Cristina},

journal = {Commentationes Mathematicae Universitatis Carolinae},

keywords = {compactifications; remainders; compactifications; remainder},

language = {eng},

number = {1},

pages = {127-136},

publisher = {Charles University in Prague, Faculty of Mathematics and Physics},

title = {A generalization of Magill's Theorem for non-locally compact spaces},

url = {http://eudml.org/doc/247720},

volume = {36},

year = {1995},

}

TY - JOUR

AU - Faulkner, Gary D.

AU - Vipera, Maria Cristina

TI - A generalization of Magill's Theorem for non-locally compact spaces

JO - Commentationes Mathematicae Universitatis Carolinae

PY - 1995

PB - Charles University in Prague, Faculty of Mathematics and Physics

VL - 36

IS - 1

SP - 127

EP - 136

AB - In the theory of compactifications, Magill's theorem that the continuous image of a remainder of a space is again a remainder is one of the most important theorems in the field. It is somewhat unfortunate that the theorem holds only in locally compact spaces. In fact, if all continuous images of a remainder are again remainders, then the space must be locally compact. This paper is a modification of Magill's result to more general spaces. This of course requires restrictions on the nature of the function.

LA - eng

KW - compactifications; remainders; compactifications; remainder

UR - http://eudml.org/doc/247720

ER -

## References

top- Caterino A., Faulkner G.D., Vipera M.C., Two applications of singular sets to the theory of compactifications, Rend. Ist. Mat. Univ. Trieste 21 (1989), 248-258. (1989) Zbl0772.54018MR1154977
- Engelking R., General Topology, Heldermann, Berlin, 1989. Zbl0684.54001MR1039321
- Magill K.D., A note on compactifications, Math. Z. 94 (1966), 322-325. (1966) Zbl0146.18501MR0203681
- Magill K.D., The lattice of compactifications of a locally compact space, Proc. London Math. Soc. 18 (1968), 231-244. (1968) Zbl0161.42201MR0229209
- Rayburn M.C., On Hausdorff compactifications, Pacific J. of Math. 44 (1973), 707-714. (1973) Zbl0257.54021MR0317277
- Fu-Chien Tzung, Sufficient conditions for the set of Hausdorff compactifications to be a lattice, Ph.D. Thesis, North Carolina State University.

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