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In this paper we study operators originated from semi-B-Fredholm theory andas a consequence we get some results regarding boundaries and connected hullsof the corresponding spectra. In particular, we prove that a bounded linearoperator $T$ acting on a Banach space, having topological uniform descent, is a{\bf BR} operator if and only if $0$ is not an accumulation point of theassociated spectrum $\sigma_{\bf R}(T)=\{\lambda\in\CC:T-\lambda I\notin {\bfR}\}$, where ${\bf R}$ denote any of the following classes: upper semi-Weyloperators, Weyl operators, upper semi-Fredholm operators, Fredholm operators,operators with finite (essential) descent and ${\bf BR}$ the B-regularityassociated to ${\bf R}$ as in \cite{P8}. Under the stronger hypothesis ofquasi-Fredholmness of $T,$ we obtain a similar characterization for $T$ being a{$\bf BR$} operator for much larger families of sets ${\bf R}.$

Toplogical uniform descent, quasi-Fredholmness and operators originated from semi-B-Fredholm theory