A decomposition of normality via a generalization of $\kappa$-normality

Ananga Kumar Das

India

Shri Mata Vaishno Devi University

Department of Mathematics

Pratibha Bhat

India

Shri Mata Vaishno Devi University

Department of Mathematics
|

Accepted: 2017-03-10

|

Published: 2017-10-02

DOI: https://doi.org/10.4995/agt.2017.4220
Funding Data

Downloads

Keywords:

regularly open set, regularly closed set, θ-open set, θ-closed set, κ-normal (mildly) normal space, almost normal space, (weakly) (functionally) θ-normal space, weakly κ-normal space, ∆-normal space, strongly seminormal space

Supporting agencies:

This research was not funded

Abstract:

A simultaneous generalization of κ-normality and weak θ-normality is introduced. Interrelation of this generalization of normality with existing variants of normality is studied. In the process of investigation a new decomposition of normality is obtained.

Show more Show less

References:

A. V. Arhangel'skii and L. Ludwig, On $alpha$-normal and $beta$-normal spaces, Comment. Math. Univ. Carolin. 42, no. 3 (2001), 507-519.

A.V. Arhangel'skii, Relative topological properties and relative topological spaces, Topology Appl. 70 (1996), 87-99.

https://doi.org/10.1016/0166-8641(95)00086-0

A. K. Das, P. Bhat and J. K. Tartir, On a simultaneous generalization of $beta$-normality and almost $beta$-normality, Filomat 31, no. 2 (2017), 425-430.

A. K. Das and P. Bhat, Decompositions of normality and interrelation among its variants, Math. Vesnik 68, 2 (2016), 77-86.

A. K. Das, P. Bhat and R. Gupta, Factorizations of normality via generalizations of normality, Mathematica Bohemica 141, no. 4 (2016), 463-473.

https://doi.org/10.21136/MB.2016.0048-15

A. K. Das and P. Bhat, A class of spaces containing all densely normal spaces, Indian J. Math. 57, no. 2 (2015), 217-224.

A. K. Das, A note on spaces between normal and $kappa$-normal spaces, Filomat 27, no. 1 (2013), 85-88.

https://doi.org/10.2298/FIL1301085D

A. K. Das, Simultaneous generalizations of regularity and normality, Eur. J. Pure Appl. Math. 4 (2011), 34-41.

A. K. Das, $Delta$-normal spaces and decompositions of normality, Applied General Topology 10, no. 2 (2009), 197-206.

https://doi.org/10.4995/agt.2009.1733

W. Just and J. Tartir, A $pi$-normal, not densely normal Tychonof spaces, Proc. Amer. Math. Soc. 127, no. 3 (1999), 901-905.

https://doi.org/10.1090/S0002-9939-99-04587-6

L. N. Kalantan, $pi$-Normal topological spaces, Filomat 22, no. 1 (2008), 173-181.

https://doi.org/10.2298/FIL0801173K

J. K. Kohli and A. K. Das, New normality axioms and decompositions of normality, Glasnik Mat. 37(57) (2002), 163-173.

J. K. Kohli and A. K. Das, A class of spaces containing all generalized absolutely closed (almost compact) spaces, Applied General Topology 7, no. 2 (2006), 233-244.

https://doi.org/10.4995/agt.2006.1926

J. K. Kohli and D. Singh, Weak normality properties and factorizations of normality, Acta Math. Hungar. 110 (2006), 67-80.

https://doi.org/10.1007/s10474-006-0007-y

C. Kuratowski, Topologie I, Hafner, New York, 1958.

P. E. Long and L. L. Herrington, The $T_theta$ topology and faintly continuous functions, Kyungpook Math. J. 22, no. 1 (1982), 7-14.

M. G. Murdeshwar, General Topology, Wiley Eastern Ltd., 1986.

M. K. Singal and S. P. Arya, On almost normal and almost completely regular spaces, Glasnik Mat. 5(25) (1970), 141-152.

M. K.Singal and A. R. Singal, Mildly normal spaces, Kyungpook Math J. 13 (1973), 27-31.

E. V. Stchepin, Real valued functions and spaces close to normal, Sib. J. Math. 13, no. 5 (1972), 1182-1196.

N. V. Velicko, H-closed topological spaces, Amer. Math. Soc, Transl. 78, no. 2, (1968), 103-118.

G. Vigilino, Seminormal and C-compact spaces, Duke J. Math. 38 (1971), 57-61.

https://doi.org/10.1215/S0012-7094-71-03808-7

V. Zaitsev, On certain classes of topological spaces and their bicompactifications, Dokl. Akad. Nauk SSSR 178 (1968), 778-779.

Show more Show less