Some Properties of Fuzzy Contractible Spaces

2014 ◽  
Vol 1 (2) ◽  
pp. 141-144
Author(s):  
Essam Hamouda ◽  
Keyword(s):  
Contractible Spaces

On the decomposition of spaces in Cartesian products and unions

1959 ◽  
Vol 55 (3) ◽  
pp. 248-256 ◽  
Author(s):  
Tudor Ganea ◽  
Peter J. Hilton
Keyword(s):  
Topological Space ◽  
Homotopy Type ◽  
General Problem ◽  
Cartesian Product ◽  
Cartesian Products ◽  
Contractible Spaces

The present paper is concerned with particular cases, obtained by suitably restricting the spaces involved, of the following general problem.Given a topological space X, we ask whether there exist integers n ≥ 2 and non-contractible spaces X1, …, Xn such that X has the homotopy type of the Cartesian product X1, × … × Xn or of the union X1, v … v Xn.

Isotopy of 2-Dimensional Cones

1966 ◽  
Vol 18 ◽  
pp. 201-210
Author(s):  
Arthur H. Copeland
Keyword(s):  
Homotopy Theory ◽  
Surprising Result ◽  
Converse Statement ◽  
Contractible Spaces

Knowing the isotopy of cones is a crucial first step in knowing the isotopy of finitely triangulable spaces, for the cones are exactly the stars of vertices. Furthermore, they are the simplest examples of contractible spaces, and the non-triviality of the contractible spaces is one of the distinguishing characteristics of isotopy theory as contrasted with homotopy theory.The present paper is concerned with the cones over 1-dimensional finitely triangulable spaces. It is clear that homeomorphic spaces have homeomorphic cones, hence cones of the same isotopy type. The surprising result of §2 is that there are very few exceptions to the converse statement. The exceptional isotopy classes of cones all contain cones over spaces that are themselves cones.

scholarly journals LECs, Local Mixers, Topological Groups and Special Products

1988 ◽  
Vol 44 (2) ◽  
pp. 252-258 ◽  
Author(s):  
Carlos R. Borges
Keyword(s):  
Topological Group ◽  
Topological Groups ◽  
Symmetric Products ◽  
Free Topological Group ◽  
Reduced Products ◽  
Contractible Spaces ◽  
Homeomorphism Groups

AbstractWe prove that every (locally) contractible topological group is (L)EC and apply these results to homeomorphism groups, free topological groups, reduced products and symmetric products. Our main results are: The free topological group of a θ-contractible space is equiconnected. A paracompact and weakly locally contractible space is locally equiconnected if and only if it has a local mixer. There exist compact metric contractible spaces X whose reduced (symmetric) products are not retracts of the Graev free topological groups F(X) (A(X)) (thus correcting results we published ibidem).

Solution set for fractional differential equations with Riemann-Liouville derivative

2013 ◽  
Vol 16 (3) ◽  
Author(s):  
Yurilev Chalco-Cano ◽  
Juan Nieto ◽  
Abdelghani Ouahab ◽  
Heriberto Román-Flores
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Solution Set ◽  
Topological Properties ◽  
Initial Value ◽  
Structure Solution ◽  
Liouville Derivative ◽  
Liouville Fractional Derivative ◽  
Fractional Differential ◽  
Contractible Spaces

AbstractWe study an initial value problem for a fractional differential equation using the Riemann-Liouville fractional derivative. We obtain some topological properties of the solution set: It is the intersection of a decreasing sequence of compact nonempty contractible spaces. We extend the classical Kneser’s theorem on the structure solution set for ordinary differential equations.

scholarly journals Some Properties of the Covariant Functor Set of Exponential Type

2021 ◽  
Vol 11 (2) ◽  
pp. 1139-1152
Author(s):  
Tursunbay Zhuraev
Keyword(s):  
Topological Space ◽  
Exponential Type ◽  
Covariant Functor ◽  
Topological Spaces ◽  
Continuous Mappings ◽  
Contractible Spaces

In this paper, it is shown that the sets of all non-empty subsets Set (x) of a topological space X with exponential topology is a covariant functor in the category of -topological spaces and their continuous mappings into itself. It is shown that the functor Set is a covariant functor in the category of topological spaces and continuous mappings into itself, a pseudometric in the space Set (x) is defined, and compact, connected, finite, and countable subspaces of Set (x) are distinguished. It also shows various kinds of connectivity, soft, locally soft, and n - soft mappings in Set (x). One interesting example is given for the TOPY category. It is proved that the functor Set maps open mappings to open, contractible and locally contractible spaces and into contractible and locally contractible spaces.

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