R z -supercontinuous functions

Davinder Singh; Brij Kishore Tyagi; Jeetendra Aggarwal; Jogendra K. Kohli

Mathematica Bohemica (2015)

  • Volume: 140, Issue: 3, page 329-343
  • ISSN: 0862-7959

Abstract

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A new class of functions called “ R z -supercontinuous functions” is introduced. Their basic properties are studied and their place in the hierarchy of strong variants of continuity that already exist in the literature is elaborated. The class of R z -supercontinuous functions properly includes the class of R cl -supercontinuous functions, Tyagi, Kohli, Singh (2013), which in its turn contains the class of cl -supercontinuous ( clopen continuous) functions, Singh (2007), Reilly, Vamanamurthy (1983), and is strictly contained in the class of R δ -supercontinuous, Kohli, Tyagi, Singh, Aggarwal (2014), which in its turn is properly contained in the class of R -supercontinuous functions, Kohli, Singh, Aggarwal (2010).

How to cite

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Singh, Davinder, et al. "$R_z$-supercontinuous functions." Mathematica Bohemica 140.3 (2015): 329-343. <http://eudml.org/doc/271592>.

@article{Singh2015,
abstract = {A new class of functions called “$R_\{z\}$-supercontinuous functions” is introduced. Their basic properties are studied and their place in the hierarchy of strong variants of continuity that already exist in the literature is elaborated. The class of $R_\{z\}$-supercontinuous functions properly includes the class of $R_\{\rm cl\}$-supercontinuous functions, Tyagi, Kohli, Singh (2013), which in its turn contains the class of $\rm cl$-supercontinuous ($\equiv $ clopen continuous) functions, Singh (2007), Reilly, Vamanamurthy (1983), and is strictly contained in the class of $R_\{\delta \}$-supercontinuous, Kohli, Tyagi, Singh, Aggarwal (2014), which in its turn is properly contained in the class of $R$-supercontinuous functions, Kohli, Singh, Aggarwal (2010).},
author = {Singh, Davinder, Tyagi, Brij Kishore, Aggarwal, Jeetendra, Kohli, Jogendra K.},
journal = {Mathematica Bohemica},
keywords = {$z$-supercontinuous function; $F$-supercontinuous function; $\rm cl$-supercontinuous function; $R_z$-supercontinuous function; $R$-supercontinuous function; $r_z$-open set; $r_z$-closed set; $z$-embedded set; $R_z$-space; functionally Hausdorff space},
language = {eng},
number = {3},
pages = {329-343},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {$R_z$-supercontinuous functions},
url = {http://eudml.org/doc/271592},
volume = {140},
year = {2015},
}

TY - JOUR
AU - Singh, Davinder
AU - Tyagi, Brij Kishore
AU - Aggarwal, Jeetendra
AU - Kohli, Jogendra K.
TI - $R_z$-supercontinuous functions
JO - Mathematica Bohemica
PY - 2015
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 140
IS - 3
SP - 329
EP - 343
AB - A new class of functions called “$R_{z}$-supercontinuous functions” is introduced. Their basic properties are studied and their place in the hierarchy of strong variants of continuity that already exist in the literature is elaborated. The class of $R_{z}$-supercontinuous functions properly includes the class of $R_{\rm cl}$-supercontinuous functions, Tyagi, Kohli, Singh (2013), which in its turn contains the class of $\rm cl$-supercontinuous ($\equiv $ clopen continuous) functions, Singh (2007), Reilly, Vamanamurthy (1983), and is strictly contained in the class of $R_{\delta }$-supercontinuous, Kohli, Tyagi, Singh, Aggarwal (2014), which in its turn is properly contained in the class of $R$-supercontinuous functions, Kohli, Singh, Aggarwal (2010).
LA - eng
KW - $z$-supercontinuous function; $F$-supercontinuous function; $\rm cl$-supercontinuous function; $R_z$-supercontinuous function; $R$-supercontinuous function; $r_z$-open set; $r_z$-closed set; $z$-embedded set; $R_z$-space; functionally Hausdorff space
UR - http://eudml.org/doc/271592
ER -

References

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