On the set function ℘

Sergio Macías

Commentationes Mathematicae Universitatis Carolinae (2024)

  • Issue: 1, page 99-129
  • ISSN: 0010-2628

Abstract

top
Inspired by the work that Professor Janusz R. Prajs did on homogeneous metric continua in his paper (2010) and the version of his work for Hausdorff continua with the uniform property of Effros done by this author, we introduce a new set function, ℘ , and present properties of it.

How to cite

top

Macías, Sergio. "On the set function $\wp $." Commentationes Mathematicae Universitatis Carolinae (2024): 99-129. <http://eudml.org/doc/299945>.

@article{Macías2024,
abstract = {Inspired by the work that Professor Janusz R. Prajs did on homogeneous metric continua in his paper (2010) and the version of his work for Hausdorff continua with the uniform property of Effros done by this author, we introduce a new set function, $\wp $, and present properties of it.},
author = {Macías, Sergio},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {additivity; almost connected im kleinen; analytic set; aposyndetic continuum; atomic map; continuum; decomposable continuum; $G_\delta $ set; hyperspace; indecomposable continuum; monotone map; property of Kelley; set function $\mathcal \{K\}$; set function $\mathcal \{T\}$; set function $\wp $; set functions continuous on continua; uniform property of Effros; upper semicontinuous function},
language = {eng},
number = {1},
pages = {99-129},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On the set function $\wp $},
url = {http://eudml.org/doc/299945},
year = {2024},
}

TY - JOUR
AU - Macías, Sergio
TI - On the set function $\wp $
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2024
PB - Charles University in Prague, Faculty of Mathematics and Physics
IS - 1
SP - 99
EP - 129
AB - Inspired by the work that Professor Janusz R. Prajs did on homogeneous metric continua in his paper (2010) and the version of his work for Hausdorff continua with the uniform property of Effros done by this author, we introduce a new set function, $\wp $, and present properties of it.
LA - eng
KW - additivity; almost connected im kleinen; analytic set; aposyndetic continuum; atomic map; continuum; decomposable continuum; $G_\delta $ set; hyperspace; indecomposable continuum; monotone map; property of Kelley; set function $\mathcal {K}$; set function $\mathcal {T}$; set function $\wp $; set functions continuous on continua; uniform property of Effros; upper semicontinuous function
UR - http://eudml.org/doc/299945
ER -

References

top
  1. Bellamy D. P., Porter K. F., 10.1090/S0002-9939-1991-1070510-X, Proc. Am. Math. Soc. 113 (1991), no. 2, 593–598. MR1070510DOI10.1090/S0002-9939-1991-1070510-X
  2. Camargo J., Macías S., 10.1007/s12346-021-00556-9, Qual. Theory Dyn. Syst. 21 (2022), no. 2, Paper No. 25, 43 pages. MR4372608DOI10.1007/s12346-021-00556-9
  3. Charatonik W. J., 10.1016/S0166-8641(98)00055-8, Topology Appl. 96 (1999), no. 3, 209–216. MR1709689DOI10.1016/S0166-8641(98)00055-8
  4. Engelking R., General Topology, Sigma Series in Pure Mathematics, 6, Heldermann Verlag, Berlin, 1989. Zbl0684.54001MR1039321
  5. Goodykoontz J. T, Jr., 10.4064/fm-95-1-1-10, Fund. Math. 95 (1977), no. 1, 1–10. MR0436097DOI10.4064/fm-95-1-1-10
  6. Gorka S., Several Set Functions and Continuous Maps, Thesis Ph.D. Dissertation, University of Delaware, Delaware, 1997. MR2696379
  7. Hagopian C. L., 10.1090/S0002-9939-1969-0247612-9, Proc. Amer. Math. Soc. 23 (1969), 615–622. MR0247612DOI10.1090/S0002-9939-1969-0247612-9
  8. Hagopian C. L., 10.1090/S0002-9947-1970-0254823-8, Trans. Amer. Math. Soc. 147 (1970), 389–402. MR0254823DOI10.1090/S0002-9947-1970-0254823-8
  9. Ingram W. T., Mahavier W. S., Inverse limits of upper semi-continuous set valued functions, Houston J. Math. 32 (2006), no. 1, 119–130. MR2202356
  10. Jones F. B., 10.2307/2372339, Amer. J. Math. 70 (1948), 403–413. MR0025161DOI10.2307/2372339
  11. Kechris A. S., Classical Descriptive Set Theory, Graduate Texts in Mathematics, 156, Springer, New York, 1995. Zbl0819.04002MR1321597
  12. Macías S., 10.1016/j.topol.2017.08.009, Topology Appl. 230 (2017), 338–352. MR3702777DOI10.1016/j.topol.2017.08.009
  13. Macías S., On Jones’ set function 𝒯 and the property of Kelley for Hausdorff continua, Topology Appl. 226 (2017), 51–65. MR3660264
  14. Macías S., Topics on Continua, Springer, Cham, 2018. MR3823258
  15. Macías S., Set Function 𝒯 - an Account on F. B. Jones’ Contributions to Topology, Developments in Mathematics, 67, Springer, Cham, 2021. MR4238567
  16. Macías S., 10.1515/ms-2023-0075, Math. Slovaca 73 (2023), no. 4, 1013–1022. MR4623271DOI10.1515/ms-2023-0075
  17. Makuchowski W., On local connectedness in hyperspaces, Bull. Polish Acad. Sci. Math. 47 (1999), no. 2, 119–126. MR1686673
  18. Mrówka S., 10.4064/fm-45-1-247-253, Fund. Math. 45 (1958), 237–346. MR0098359DOI10.4064/fm-45-1-247-253
  19. Nadler S. B., Jr., Hyperspaces of Sets: A Text with Research Questions, Aportaciones Matemáticas: Textos, 33, Sociedad Matemática Mexicana, México, 2006. MR2293338
  20. Prajs J. R., 10.4153/CJM-2010-010-4, Canad. J. Math. 62 (2010), no. 1, 182–201. MR2597029DOI10.4153/CJM-2010-010-4
  21. Rogers J. T., Jr., 10.1090/S0002-9939-1985-0806092-1, Proc. Amer. Math. Soc. 95 (1985), no. 3, 483–486. MR0806092DOI10.1090/S0002-9939-1985-0806092-1
  22. Rogers J. T., Jr., 10.1090/S0002-9939-03-06888-6, Proc. Amer. Math. Soc. 131 (2003), no. 10, 3285–3288. MR1992870DOI10.1090/S0002-9939-03-06888-6
  23. Willard S., General Topology, Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, 1970. Zbl1052.54001MR0264581

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.