scholarly journals The Cech homology theory in the category of soft topological spaces

2020 ◽  
Vol 1 (1) ◽  
pp. 41-51
Author(s):  
Cigdem Gunduz Aras ? · Sebuhi Abdullayev
Keyword(s):  
Homology Theory ◽  
Topological Spaces ◽  
Čech Homology

Closed Coverings in Cech Homology Theory

1957 ◽  
Vol 84 (2) ◽  
pp. 319
Author(s):  
E. E. Floyd
Keyword(s):  
Homology Theory ◽  
Čech Homology

Generalized functions and Čech homology theory

1966 ◽  
Vol 72 (1) ◽  
pp. 45-57 ◽  
Author(s):  
Rubens G. Lintz
Keyword(s):  
Homology Theory ◽  
Generalized Functions ◽  
Čech Homology

IX. The Čech homology theory

1952 ◽  
pp. 233-256
Keyword(s):  
Homology Theory ◽  
Čech Homology

scholarly journals Closed coverings in Čech homology theory

1957 ◽  
Vol 84 (2) ◽  
pp. 319-319
Author(s):  
E. E. Floyd
Keyword(s):  
Homology Theory ◽  
Čech Homology

Singular homology theory in the category of soft topological spaces

2015 ◽  
Vol 22 (4) ◽  
Author(s):  
Sadi Bayramov ◽  
Cigdem Gündüz (Aras) ◽  
Leonard Mdzinarishvili
Keyword(s):  
Homology Group ◽  
Homology Theory ◽  
Topological Spaces ◽  
Homology Groups ◽  
Relative Homology ◽  
Singular Homology

AbstractIn the category of soft topological spaces, a singular homology group is defined and the homotopic invariance of this group is proved [Internat. J. Engrg. Innovative Tech. (IJEIT) 3 (2013), no. 2, 292–299]. The first aim of this study is to define relative homology groups in the category of pairs of soft topological spaces. For these groups it is proved that the axioms of dimensional and exactness homological sequences hold true. The axiom of excision for singular homology groups is also proved.

Hyper(co)homology for exact left covariant functors and a homology theory for topological spaces

1995 ◽  
Vol 50 (3) ◽  
pp. 575-611 ◽  
Author(s):  
E G Sklyarenko
Keyword(s):  
Homology Theory ◽  
Topological Spaces

The Homology of Uniform Spaces

1973 ◽  
Vol 25 (3) ◽  
pp. 449-455 ◽  
Author(s):  
Mohammed Bahauddin ◽  
John Thomas
Keyword(s):  
Algebraic Topology ◽  
Uniform Space ◽  
Topological Spaces ◽  
Dimension Theory ◽  
Uniform Spaces ◽  
The Past ◽  
Body Of Knowledge ◽  
Čech Homology ◽  
Group A ◽  
Cech Cohomology

In the past thirty years, algebraic topologists have developed a great body of knowledge concerning the category of topological spaces. By contrast, corresponding problems in the category of uniform spaces have been barely touched. Lubkin [8] studied the notion of a covering space in the category of generalized uniform spaces, and suggested that much of algebraic topology could be profitably studied in this category. Deming [2] discussed the fundamental group of a generalized uniform space, and related it to the first Čech homology group. A slightly different version of Cech cohomology was defined by Kuzminov and Svedov in [7] and related to the dimension theory of uniform spaces.

scholarly journals A characterization of the Čech homology theory

1970 ◽  
Vol 21 (2) ◽  
pp. 229-237 ◽  
Author(s):  
S. K. Kaul
Keyword(s):  
Homology Theory ◽  
Čech Homology

A Geometric Approach to Homology Theory

1976 ◽  
Author(s):  
S. Buonchristiano ◽  
C. P. Rourke ◽  
B. J. Sanderson
Keyword(s):  
Geometric Approach ◽  
Homology Theory
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