Normality in k-and-ℵ spaces

Mapping theorems on א-spaces

In this paper we improve some mapping theorems on א-spaces. For instance we show that an א-space is preserved by a closed and countably bi-quotient map. This is an improvement of Yun Ziqiu’s theorem: an א-space is preserved by a closed and open map.

σ-Normality of Topological Spaces

σ-normality of topological spaces

Continuous $ k $-Frames and their Dual in Hilbert Spaces

The notion of $k$-frames was recently introduced by Gu avruc ta in Hilbert  spaces to study atomic systems with respect to a bounded linear operator. A continuous frame is a family of vectors in a Hilbert space which allows reproductions of arbitrary elements by continuous super positions. In this manuscript, we construct a continuous $k$-frame, so called c$k$-frame along with an atomic system ...

Continuous $k$-Fusion Frames in Hilbert Spaces

The study of the c$k$-fusions frames shows that the emphasis on the measure spaces introduces a new idea, although some similar properties with the discrete case are raised. Moreover, due to the nature of measure spaces, we have to use new techniques for new results. Especially, the topic of the dual of frames  which is important for frame applications, have been specified  completely for the c...