On Topologized Fundamental Groups with Small Loop Transfer Viewpoints

Jamali, Noorollah; Mashayekhy, Behrooz; Torabi, Hamid; Pashaei, Seyyed Zeynal; Rashid, Mehdi Abdullahi

doi:10.48550/arxiv.1708.02606

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Relationship Between Strong Slt Spaces and Covering Maps1

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2019

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“…Recall that Jamali et al in [11,Proposition 3.2] proved that the equality of the first inequality of the above chain holds in SLT spaces at x 0 . In the following we are going to present some conditions for the equality of the others inequalities.…”

Section: Relationship Between Strong Slt Spaces and Covering Mapsmentioning

confidence: 99%

On strong small loop transfer spaces relative to subgroups of fundamental groups

Pashaei

Mashayekhy

Torabi

et al. 2019

Topology and its Applications

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Let H be a subgroup of the fundamental group π 1 (X, x 0 ). By extending the concept of strong SLT space to a relative version with respect to H, strong H-SLT space, first, we investigate the existence of a covering map for strong H-SLT spaces. Moreover, we show that a semicovering map is a covering map in the presence of strong H-SLT property. Second, we present conditions under which the whisker topology agrees with the lasso topology on X H . Also, we study the relationship between open subsets of π wh 1 (X, x 0 ) and π l 1 (X, x 0 ). Finally, we give some examples to justify the definition and study of strong H-SLT spaces.

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Section: Relationship Between Strong Slt Spaces and Covering Mapsmentioning

confidence: 99%