Compact matrix operators on a new sequence space related to ℓp
... For the reader’s convenience, we list a few well-known definitions and results concerning the Hausdorff measure of noncompactness which can be found in [, ], and []. Let S and M be subsets of a metric space (X, d) and ε > . Then S is called an ε-net of M in X if for every x ∈ M there exists s ∈ S ...
... For the reader’s convenience, we list a few well-known definitions and results concerning the Hausdorff measure of noncompactness which can be found in [, ], and []. Let S and M be subsets of a metric space (X, d) and ε > . Then S is called an ε-net of M in X if for every x ∈ M there exists s ∈ S ...
229 NEARLY CONTINUOUS MULTIFUNCTIONS 1. Introduction
... such that x ∈ F − (V ) (x ∈ F + (V )), there exists an open set U containing x such that U ⊆ F − (V ) (U ⊆ F + (V )). The following theorem give us some characterizations of lower (upper) nearly continuous multifunction. We know that a net (xα ) in a topological space (X, τ ) is called eventually in ...
... such that x ∈ F − (V ) (x ∈ F + (V )), there exists an open set U containing x such that U ⊆ F − (V ) (U ⊆ F + (V )). The following theorem give us some characterizations of lower (upper) nearly continuous multifunction. We know that a net (xα ) in a topological space (X, τ ) is called eventually in ...
CATEGORICAL PROPERTY OF INTUITIONISTIC TOPOLOGICAL
... short) and any IS in T is called an intuitionistic open set (IOS for short) in X. The complement A of an IOS A is called an intuitionistic closed set (ICS for short) in X. Example 2.5. For any topological space (X, τ ), we trivially have an ITS (X, T ), where T = {hX, A, Ac i | A ∈ τ }. Example 2.6. ...
... short) and any IS in T is called an intuitionistic open set (IOS for short) in X. The complement A of an IOS A is called an intuitionistic closed set (ICS for short) in X. Example 2.5. For any topological space (X, τ ), we trivially have an ITS (X, T ), where T = {hX, A, Ac i | A ∈ τ }. Example 2.6. ...
Spectra for commutative algebraists.
... Traditional commutative algebra considers commutative rings R and modules over them, but some constructions make it natural to extend further to considering chain complexes of R-modules; the need to consider robust, homotopy invariant properties leads to the derived category D(R). Once we admit chai ...
... Traditional commutative algebra considers commutative rings R and modules over them, but some constructions make it natural to extend further to considering chain complexes of R-modules; the need to consider robust, homotopy invariant properties leads to the derived category D(R). Once we admit chai ...
