Sifat-sifat Fungsi Terfragmentasi dan Fungsi Terfragmentasi Terhitung Fungsional

Albert Mario Kumanireng, Atok Zulijanto

Abstract


Pada artikel ini, diteliti sifat-sifat fungsi terfragmentasi dan fungsi terfragmentasi terhitung fungsional. Dengan menggunakan barisan \textit{transfinite} regular, dibuktikan bahwa himpunan semua fungsi terfragmentasi bernilai real dan himpunan semua fungsi terfragmentasi terhitung fungsional dan terbatas yang bernilai real merupakan ring. Selain itu, dibuktikan pula sifat fungsi terfragmentasi dan fungsi terfragmentasi terhitung fungsional yang analog dengan Teroema Weierstrass M-Test. Lebih lanjut, diberikan syarat tambahan supaya fungsi terfragmentasi terhitung fungsional juga kontinu.

Keywords


fungsi terfragmentasi-$\epsilon$, fungsi terfragmentasi, fungsi terfragmentasi terhitung fungsional, fungsi terfragmentasi terhitung-$\epsilon$ fungsional, barisan regular.

Full Text:

PDF

References


Dugundji, J., 1967, {it Topology}, Allyn and Bacon, Inc., Boston.

Engelking, R., 1989, {it General Topology}, Heldermann Verlag, Berlin.

Kalenda, O.F.K. and Spurny, J., 2005, Extending Baire-One Function on Topological Space, {em Topology and Its Applications}, Volume 149, Pages 195-216.

Karlova, O. and Mykhaylyuk, V., 2019, Extension of Fragmented Baire-One Function on Lindel"{o}f Spaces, {em Topology and Its Applications}, Volume 253, Pages 85-94.

Karlova, O. and Mykhaylyuk, V., 2020, Extending Baire-One Function on Compat Spaces, {em Topology and Its Applications}, Volume 277, Pages 1-9.

A Generalization of Functions of The First Class, {em Topology and Its Applications}, Volume 50, Pages 217-239.

Kuratowski, K., 1966, {it Topology 1}, Academis Press, New York. -

Leung. D.H. and Tang. W-K., 2006, Extension of functions with Small Oscillation, {em Fund. Math.}, Volume 192, Pages 183-193.

Spurny, J., 2005, Affine Baire-One Functions on Choquet Simplexes, {em Bull. Austral. Math. Soc}, Volume 71, Pages 235-258.




DOI: https://doi.org/10.24198/jmi.v19.n1.45047.55-66

Refbacks

  • There are currently no refbacks.


Copyright (c) 2023 Jurnal Matematika Integratif

Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

Published By:

Department of Matematics, FMIPA, Universitas Padjadjaran, Jl. Raya Bandung-Sumedang KM. 21 Jatinangor


Indexed by:

width=width= width= width= width= width=

 

Visitor Number : free hit counter View My Stats


Creative Commons License
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.