1980 Mathematical Subject Classification Code. 54A20
... In 1970, G. D. Richardson [21] and J. F. Ramaley and O. Wyler [15] published different versions of a ...
... In 1970, G. D. Richardson [21] and J. F. Ramaley and O. Wyler [15] published different versions of a ...
IV.2 Homology
... denoted as Zp ≤ Cp , which is a subgroup of the group of p-chains. In other words, the group of p-cycles is the kernel of the p-th boundary homomorphism, Zp = ker ∂p . Since the chain groups are abelian so are their cycle subgroups. Consider p = 0 as an example. The boundary of every vertex is zero, ...
... denoted as Zp ≤ Cp , which is a subgroup of the group of p-chains. In other words, the group of p-cycles is the kernel of the p-th boundary homomorphism, Zp = ker ∂p . Since the chain groups are abelian so are their cycle subgroups. Consider p = 0 as an example. The boundary of every vertex is zero, ...
g-COMPACTNESS LIKE PROPERTIES IN GENERALIZED
... N−{1, 2, 3}, then clg (M ) = N −{1, 2, 3} and intg (clg (M )) = ∅. If M = M1 ∪ {2} or M = M1 ∪ {3}, where M1 ⊆ N − {1, 2, 3}, then clg (M ) is either N−{1, 2} or N−{1, 3} and intg (clg (M )) = ∅. If M is not a singleton subset of N containing {1} and M ∈ / g, then clg (M ) = N and M * intg (clg (M ) ...
... N−{1, 2, 3}, then clg (M ) = N −{1, 2, 3} and intg (clg (M )) = ∅. If M = M1 ∪ {2} or M = M1 ∪ {3}, where M1 ⊆ N − {1, 2, 3}, then clg (M ) is either N−{1, 2} or N−{1, 3} and intg (clg (M )) = ∅. If M is not a singleton subset of N containing {1} and M ∈ / g, then clg (M ) = N and M * intg (clg (M ) ...
Topologies on the Set of Borel Maps of Class α
... The following properties of Borel maps of class α are known (see, for example, [4] and [9]): (1) A map f is of class 0 if and only if f is continuous. (2) The maps of class α are also of class β, for all β > α. (3) If f is of class α, 1 of class β, and 1 ◦ f is defined, then the map 1 ◦ f is of clas ...
... The following properties of Borel maps of class α are known (see, for example, [4] and [9]): (1) A map f is of class 0 if and only if f is continuous. (2) The maps of class α are also of class β, for all β > α. (3) If f is of class α, 1 of class β, and 1 ◦ f is defined, then the map 1 ◦ f is of clas ...
this PDF file - European Journal of Pure and Applied
... b-continuity was brought out by Sayed.et.al [8] in 2010. Recently Krishnaveni and Vigneshwaran [4] came out with supra bT -closed sets and defined their properties. In 2013, Jamal M.Mustafa.et.al[3] came out with the concect of supra b- connected and supra bLindelof spaces. Now we bring up with the ...
... b-continuity was brought out by Sayed.et.al [8] in 2010. Recently Krishnaveni and Vigneshwaran [4] came out with supra bT -closed sets and defined their properties. In 2013, Jamal M.Mustafa.et.al[3] came out with the concect of supra b- connected and supra bLindelof spaces. Now we bring up with the ...
APPROACHING METRIC DOMAINS Introduction Domain theory is
... of “[0, ∞]-enriched topological spaces” in a similar fashion as domain theory is supported by topology, where by “[0, ∞]-enriched topological spaces” we understand Lowen’s approach spaces [Lowen, 1997]. (In a nutshell, an approach space is to a topological space what a metric space is to an ordered ...
... of “[0, ∞]-enriched topological spaces” in a similar fashion as domain theory is supported by topology, where by “[0, ∞]-enriched topological spaces” we understand Lowen’s approach spaces [Lowen, 1997]. (In a nutshell, an approach space is to a topological space what a metric space is to an ordered ...
Sequential Separability vs Selective Sequential
... where S is the family of all sequentially dense subspaces of X. An immediate consequence of Definition 1.2 is: Proposition 1.3. Every sequentially dense subspace of a selectively sequentially separable space is sequentially separable. In particular, every selectively sequentially separable space is ...
... where S is the family of all sequentially dense subspaces of X. An immediate consequence of Definition 1.2 is: Proposition 1.3. Every sequentially dense subspace of a selectively sequentially separable space is sequentially separable. In particular, every selectively sequentially separable space is ...
General topology
In mathematics, general topology is the branch of topology that deals with the basic set-theoretic definitions and constructions used in topology. It is the foundation of most other branches of topology, including differential topology, geometric topology, and algebraic topology. Another name for general topology is point-set topology.The fundamental concepts in point-set topology are continuity, compactness, and connectedness: Continuous functions, intuitively, take nearby points to nearby points. Compact sets are those that can be covered by finitely many sets of arbitrarily small size. Connected sets are sets that cannot be divided into two pieces that are far apart. The words 'nearby', 'arbitrarily small', and 'far apart' can all be made precise by using open sets, as described below. If we change the definition of 'open set', we change what continuous functions, compact sets, and connected sets are. Each choice of definition for 'open set' is called a topology. A set with a topology is called a topological space.Metric spaces are an important class of topological spaces where distances can be assigned a number called a metric. Having a metric simplifies many proofs, and many of the most common topological spaces are metric spaces.