scholarly journals θ-R-continuous functions

1994 ◽  
Vol 17 (1) ◽  
pp. 73-78
Author(s):  
C. W. Baker
Keyword(s):  
Continuous Functions ◽  
Strong Form ◽  
Closed Graph ◽  
Graph Properties

A strong form of continuity, calledθ-R-continuity, is introduced. It is shown thatθ-R-continuity is stronger thanR-continuity. Relationships betweenθ-R-continuity and various closed graph properties are investigated. Additional properties ofθ-R-continuous functions are established.

scholarly journals R-continuous functions

1992 ◽  
Vol 15 (1) ◽  
pp. 57-64 ◽  
Author(s):  
Ch. Konstadilaki-Savvapoulou ◽  
D. Janković
Keyword(s):  
Continuous Functions ◽  
Strong Form ◽  
Topological Spaces ◽  
Strong Continuity ◽  
Closed Graph ◽  
Continuity Properties

A strong form of continuity of functions between topological spaces is introduced and studied. It is shown that in many known results, especially closed graph theorems, functions under consideration areR-continuous. Several results in the literature concerning strong continuity properties are generalized and/or improved.

A Regular Space on Which Every Real-Valued Function with a Closed Graph is Constant

1989 ◽  
Vol 32 (4) ◽  
pp. 417-424 ◽  
Author(s):  
Ivan Baggs
Keyword(s):  
Continuous Function ◽  
Continuous Functions ◽  
Regular Space ◽  
Closed Graph

AbstractAn example is given of a regular space on which every real-valued function with a closed graph is constant. It was previously known that there are regular spaces on which every continuous function is constant. It is also shown here that there are regular spaces that support only constant real-valued continuous functions, but support non-constant real-valued functions with a closed graph.

scholarly journals Quasi cl-supercontinuous functions and their function spaces

2012 ◽  
Vol 45 (3) ◽  
Author(s):  
J. K. Kohli ◽  
Jeetendra Aggarwal
Keyword(s):  
Continuous Functions ◽  
Function Spaces ◽  
Strong Form ◽  
General Topology ◽  
Regular Space ◽  
Basic Properties ◽  
New Class ◽  
Mathematical Literature ◽  
Class Of Functions ◽  
Appl Math

AbstractA 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

scholarly journals rc-continuous functions and functions with rc-strongly closed graph

2003 ◽  
Vol 2003 (72) ◽  
pp. 4547-4555
Author(s):  
Bassam Al-Nashef
Keyword(s):  
Continuous Function ◽  
Topological Space ◽  
Continuous Functions ◽  
Closed Graph ◽  
Compact Spaces ◽  
Extremally Disconnected ◽  
The Family ◽  
Regular Closed

The family of regular closed subsets of a topological space is used to introduce two concepts concerning a functionffrom a spaceXto a spaceY. The first of them is the notion offbeing rc-continuous. One of the established results states that a spaceYis extremally disconnected if and only if each continuous function from a spaceXtoYis rc-continuous. The second concept studied is the notion of a functionfhaving an rc-strongly closed graph. Also one of the established results characterizes rc-compact spaces (≡S-closed spaces) in terms of functions that possess rc-strongly closed graph.

scholarly journals Quantum Query Complexity of Minor-Closed Graph Properties

2012 ◽  
Vol 41 (6) ◽  
pp. 1426-1450 ◽  
Author(s):  
Andrew M. Childs ◽  
Robin Kothari
Keyword(s):  
Query Complexity ◽  
Closed Graph ◽  
Quantum Query Complexity ◽  
Graph Properties ◽  
Quantum Query

scholarly journals Maximal classes for the family of quasi-continuous functions with closed graph

2009 ◽  
Vol 42 (1) ◽  
Author(s):  
Waldemar Sieg
Keyword(s):  
Continuous Functions ◽  
Closed Graph ◽  
The Family

AbstractIn this paper we consider classes of functions

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