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On various classes of bitopological spaces
-
Badri P. Dvalishvili
Published/Copyright:
September 18, 2012
Abstract.
Bitopological spaces
in which every subset is 
-open in its 
-closure (i.e., (i,j)-submaximal spaces) are introduced and their properties are studied.
Based on the investigations by Arhangel'skiĭ, Collins and the author,
the necessary conditions are found for bitopological spaces to be p-connected.
Furthermore, (i,j)-I-spaces are introduced and the relations between (i,j)-submaximal, (i,j)-nodec and (i,j)-I-spaces are established when two topologies on a set are either independent of each other or interconnected by the inclusion, 
-, 
- and 
-relations.
The preservation of (i,j)-submaximal and (2,1)-I-spaces under morphisms is also considered.
Keywords: (i,j)-submaximal space; (i,j)-TD-space; (i,j)-strongly σ-discrete space; (i,j)-nodec space; (i,j)-I-space; (i,j)-locally closed quotient
Received: 2009-06-07
Revised: 2011-09-21
Published Online: 2012-09-18
Published in Print: 2012-09-01
© 2012 by Walter de Gruyter Berlin Boston
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Keywords for this article
(i,j)-submaximal space;
(i,j)-TD-space;
(i,j)-strongly σ-discrete space;
(i,j)-nodec space;
(i,j)-I-space;
(i,j)-locally closed quotient
Articles in the same Issue
- Masthead
- The Plemelj–Privalov theorem in variable exponent Clifford analysis
- Almost everywhere convergence of a subsequence of logarithmic means of Fourier series on the group of 2-adic integers
- Identities and generating functions on Chebyshev polynomials
- Left annihilators of power values of commutators with generalized derivations
- On various classes of bitopological spaces
- On P-torsion modules over a pullback of two Dedekind domains
- A remark on a polynomial matrix factorization theorem
- Convergence of double Fourier series and generalized Λ-variation
- On monoids of monotone injective partial selfmaps of integers with cofinite domains and images
- On the boundedness of product kernel operators with measures
- A new class of generalized Hermite–Bernoulli polynomials
- Global nonexistence and stability of solutions of inverse problems for a class of Petrovsky systems
- Comment on the sums
