J. K. Kohli

Fuzzy prime spectrum of a ring II

Abstract Various topological properties of the fuzzy prime spectrum of a ring and certain of its subspaces as well as its functorial nature are discussed.

A class of mappings containing all continuous and all semiconnected mappings

A function f: X -* Y is called s-continuous if for each x E X and each open set V containing f(x) and having connected complement there is an open set U containing x such that f( U) c V. In this paper basic properties of s-continuous functions are studied; conditions on domain and/or range implying continuity of s-continuous functions are obtained which generalize recent theorems of Jones, Lee and Long on semiconnected functions. Improvements of recent results of Hagan, Kohli and Long concerning the continuity of certain connected functions follow as a consequence. Also characterizations of semilocally connected spaces in terms of s-continuous functions are obtained.

Rδ-Supercontinuous Functions

Abstract A new class of functions called ‘Rδ-supercontinuous functions’ is introduced. Their basic properties are studied and their place in the hierarchy of strong variants of continuity which already exist in the literature is elaborated. The class of Rδ-supercontinuous functions (Math. Bohem., to appear) properly contains the class of Rz-supercontinuous functions which in its turn properly contains the class of Rcl- supercontinuous functions (Demonstratio Math. 46(1) (2013), 229-244) and so includes all Rcl-supercontinuous (≡clopen continuous) functions (Applied Gen. Topol. 8(2) (2007), 293-300; Indian J. Pure Appl. Math. 14(6) (1983), 767-772) and is properly contained in the class of R-supercontinuous functions (Demonstratio Math. 43(3) (2010), 703-723).

Zero dimensional and strongly zero dimensional fuzzy topological spaces

Abstract Concepts of zero dimensionality, strong zero dimensionality and total disconnectedness are extended to fuzzy topological spaces. Their basic properties and interrelationships among them are studied. A sum theorem for strongly zero dimensional fuzzy topological spaces is also obtained.

On fuzzy inner product spaces and fuzzy co-inner product spaces

Abstract The notions of fuzzy co-norm and fuzzy co-orthogonality are introduced by formulating the notion of a fuzzy co-inner product space; and their basic properties are studied.

Fuzzy topologies on function spaces

In this paper, we introduce and study three different fuzzy topologies on a given function space.

Closedness of certain classes of functions in the topology of uniform convergence

Abstract In this paper, closedness of certain classes of functions in YX in the topology of uniform convergence is observed. In particular, we show that the function spaces SC(X, Y) of quasi continuous (≡semi-continuous) functions, Cα(X, Y) of α-continuous functions and L(X, Y) of cl-supercontinuous functions are closed in YX in the topology of uniform convergence.

Quasi cl-supercontinuous functions and their function spaces

Abstract A new class of functions called ‘quasi cl-supercontinuous functions’ is introduced. Basic properties of quasi cl-supercontinuous functions are studied and their place in the hierarchy of variants of continuity that already exist in the mathematical literature is elaborated. The notion of quasi cl-supercontinuity, in general, is independent of continuity but coincides with cl-supercontinuity (≡ clopen continuity) (Applied General Topology 8(2) (2007), 293–300; Indian J. Pure Appl. Math. 14(6) (1983), 767–772), a significantly strong form of continuity, if range is a regular space. The class of quasi cl-supercontinuous functions properly contains each of the classes of (i) quasi perfectly continuous functions and (ii) almost cl-supercontinuous functions; and is strictly contained in the class of quasi z-supercontinuous functions. Moreover, it is shown that if X is sum connected (e.g. connected or locally connected) and Y is Hausdorff, then the function space Lq(X, Y) of all quasi cl-supercontinuous functions as well as the function space Lδ(X, Y) of all almost cl-supercontinuous functions from X to Y is closed in YX in the topology of pointwise convergence.

Overlapping families and covering dimension in fuzzy topological spaces

Abstract A non-classical approach is used to introduce notions of overlapping families of fuzzy sets and the order of a family of fuzzy sets leading to a coherent theory of covering dimension in fuzzy topological spaces. Class of semicrisp fuzzy topological spaces is introduced which provides a suitable framework for the study of dimension function in the fuzzy setting.

Upper and lower almost cl-supercontinuous multifunctions

Abstract The notion of almost cl-supercontinuity (≡ almost clopen continuity) of functions (Acta Math. Hungar. 107 (2005), 193–206; Applied Gen. Topology 10 (1) (2009), 1–12) is extended to the realm of multifunctions. Basic properties of upper (lower) almost cl-supercontinuous multifunctions are studied and their place in the hierarchy of strong variants of continuity of multifunctions is discussed. Examples are included to reflect upon the distinctiveness of upper (lower) almost cl-supercontinuity of multifunctions from that of other strong variants of continuity of multifunctions which already exist in the literature.