Generalized rough topological spaces
... The problem of imperfect knowledge has been tackled for a long time by philosophers, logicians and mathematicians. Recently it became also a crucial issue for computer scientists, particularly in the area of artificial intelligence. There are many approaches to the problem of how to understand and m ...
... The problem of imperfect knowledge has been tackled for a long time by philosophers, logicians and mathematicians. Recently it became also a crucial issue for computer scientists, particularly in the area of artificial intelligence. There are many approaches to the problem of how to understand and m ...
Topology I - School of Mathematics
... space or regarded as existing independently (manifolds); or sometimes subsets of a more general nature of a Euclidean space or manifold, or even of an infinite-dimensional space of functions. Although it is not possible to give a precise general definition of “topological property” (“topological inv ...
... space or regarded as existing independently (manifolds); or sometimes subsets of a more general nature of a Euclidean space or manifold, or even of an infinite-dimensional space of functions. Although it is not possible to give a precise general definition of “topological property” (“topological inv ...
Lecture Notes on Smale Spaces
... if the periodic points of X are dense, then every point is non-wandering. Proposition 1.1.3. Let X be a topological space and let f be a homeomorphism of X. 1. The set of non-wandering points is f -invariant: that is, x is nonwandering if and only if f (x) is also. 2. The set of non-wandering points ...
... if the periodic points of X are dense, then every point is non-wandering. Proposition 1.1.3. Let X be a topological space and let f be a homeomorphism of X. 1. The set of non-wandering points is f -invariant: that is, x is nonwandering if and only if f (x) is also. 2. The set of non-wandering points ...
$\ alpha $-compact fuzzy topological spaces
... of X is called an a-covering of X iff v covers X and v C Fa(X). Definition 2 . 3 . A fuzzy topological space (X, T) is said to be a-compact if every a-open cover of X has a finite subcover. D e f i n i t i o n 2.4. Let (X,T) and (Y, S) be fuzzy topological spaces. A mapping / : X -4 Y is called fuzz ...
... of X is called an a-covering of X iff v covers X and v C Fa(X). Definition 2 . 3 . A fuzzy topological space (X, T) is said to be a-compact if every a-open cover of X has a finite subcover. D e f i n i t i o n 2.4. Let (X,T) and (Y, S) be fuzzy topological spaces. A mapping / : X -4 Y is called fuzz ...
Chapter VI. Fundamental Group
... 29.L. Prove that, like free homotopy, A-homotopy is an equivalence relation. The classes into which A-homotopy splits the set of continuous maps X → Y that agree on A with a map f : A → Y are A-homotopy classes of continuous extensions of f to X. 29.M. For what A is a rectilinear homotopy fixed on A ...
... 29.L. Prove that, like free homotopy, A-homotopy is an equivalence relation. The classes into which A-homotopy splits the set of continuous maps X → Y that agree on A with a map f : A → Y are A-homotopy classes of continuous extensions of f to X. 29.M. For what A is a rectilinear homotopy fixed on A ...