Papers by hadi passandideh
Topology and its Applications, 2015
Filomat, 2021
In this paper, we introduce the based and unbased n-Spanier groups and n-semilocally simply conne... more In this paper, we introduce the based and unbased n-Spanier groups and n-semilocally simply connected spaces, and investigate their relationship. We show that under some conditions, vanishing of the n-Spanier group with respect to an open cover is equivalent to the n-semilocal simple connectivity of that space, and vice versa.
In this paper we introduce the notion of fundamental group for soft topological spaces. To do so,... more In this paper we introduce the notion of fundamental group for soft topological spaces. To do so, we define soft paths, soft loops and the notion of ξ-soft path homotopy, and study some of their basic properties. We also show that the fundamental group of an ε-soft topological group is commutative, and that π sof t 1 is a functor between the category of soft topological spaces and the category of groups.
Topology and its Applications, 2011
The aim of this paper is to discuss the homotopy properties of locally well-behaved spaces. First... more The aim of this paper is to discuss the homotopy properties of locally well-behaved spaces. First, we state a nerve theorem. It gives sufficient conditions under which there is a weak n-equivalence between the nerve of a good cover and its underlying space. Then we conclude that for any (n − 1)-connected, locally (n − 1)-connected compact metric space X which is also n-semilocally simply connected, the nth homotopy group of X, π n (X), is finitely presented. This result allows us to provide a new proof for a generalization of Shelah's theorem (Shelah, 1988 [18]) to higher homotopy groups (Ghane and Hamed, 2009 [8]). Also, we clarify the relationship between two homotopy properties of a topological space X, the property of being n-homotopically Hausdorff and the property of being n-semilocally simply connected. Further, we give a way to recognize a nullhomotopic 2-loop in 2-dimensional spaces. This result will involve the concept of generalized dendrite which introduce here. Finally, we prove that each 2-loop is homotopic to a reduced 2-loop.
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Papers by hadi passandideh