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

Abstract

top
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.

How to cite

top

Faulkner, 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
  1. 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
  2. Engelking R., General Topology, Heldermann, Berlin, 1989. Zbl0684.54001MR1039321
  3. Magill K.D., A note on compactifications, Math. Z. 94 (1966), 322-325. (1966) Zbl0146.18501MR0203681
  4. Magill K.D., The lattice of compactifications of a locally compact space, Proc. London Math. Soc. 18 (1968), 231-244. (1968) Zbl0161.42201MR0229209
  5. Rayburn M.C., On Hausdorff compactifications, Pacific J. of Math. 44 (1973), 707-714. (1973) Zbl0257.54021MR0317277
  6. Fu-Chien Tzung, Sufficient conditions for the set of Hausdorff compactifications to be a lattice, Ph.D. Thesis, North Carolina State University. 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.