Topological Spaces Over Algorithmic Representations of Universal Algebras

2020 ◽  
Vol 245 (3) ◽  
pp. 311-322
Author(s):  
N. Kh. Kasymov ◽  
I. A. Khodzhamuratova
Keyword(s):  
Topological Spaces ◽  
Universal Algebras

VARIETIES OF EQUALITY STRUCTURES

2003 ◽  
Vol 13 (04) ◽  
pp. 463-480 ◽  
Author(s):  
DESMOND FEARNLEY-SANDER ◽  
TIM STOKES
Keyword(s):  
Binary Operation ◽  
Topological Spaces ◽  
Natural Conditions ◽  
Universal Algebras ◽  
Natural Way

We consider universal algebras which are monoids and which have a binary operation we call internalized equality, satisfying some natural conditions. We show that the class of such E-structures has a characterization in terms of a distinguished submonoid which is a semilattice. Some important varieties (and variety-like classes) of E-structures are considered, including E-semilattices (which we represent in terms of topological spaces), E-rings (which we show are equivalent to rings with a generalized interior operation), E-quantales (where internalized equalities on a fixed quantale in which 1 is the largest element are shown to correspond to sublocales of the quantale), and EI-structures (in which an internalized inequality is defined and interacts in a natural way with the equality operation).

ON ir-CLOSED SETS IN TOPOLOGICAL SPACES

2020 ◽  
Vol 9 (5) ◽  
pp. 2573-2582
Author(s):  
A. M. Anto ◽  
G. S. Rekha ◽  
M. Mallayya
Keyword(s):  
Topological Spaces ◽  
Closed Sets

ON A NEW CLASS OF SEMI GENERALIZED CLOSED SETS IN STRONG GENERALIZED TOPOLOGICAL SPACES

2020 ◽  
Vol 9 (11) ◽  
pp. 9353-9360
Author(s):  
G. Selvi ◽  
I. Rajasekaran
Keyword(s):  
Topological Spaces ◽  
Closed Set ◽  
Basic Properties ◽  
Closed Sets ◽  
New Class ◽  
Open Set ◽  
Continuous Maps

This paper deals with the concepts of semi generalized closed sets in strong generalized topological spaces such as $sg^{\star \star}_\mu$-closed set, $sg^{\star \star}_\mu$-open set, $g^{\star \star}_\mu$-closed set, $g^{\star \star}_\mu$-open set and studied some of its basic properties included with $sg^{\star \star}_\mu$-continuous maps, $sg^{\star \star}_\mu$-irresolute maps and $T_\frac{1}{2}$-space in strong generalized topological spaces.

ON CONTRA SOFT ARS CLOSED SETS IN SOFT TOPOLOGICAL SPACES

2020 ◽  
Vol 9 (3) ◽  
pp. 921-926
Author(s):  
P. Anbarasi Rodrigo ◽  
K. Rajendra Suba
Keyword(s):  
Topological Spaces ◽  
Closed Sets

ON BIPOLAR FUZZY ROUGH TOPOLOGICAL SPACES

2020 ◽  
Vol 9 (11) ◽  
pp. 9733-9738
Author(s):  
S. Anita Shanthi ◽  
M. Saranya
Keyword(s):  
Topological Spaces
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