In this paper the concept of metacompactness in L-topologicalspaces is introduced by means of point finite families of L-fuzzy sets. Thisfuzzy metacompactness is a natural generalization of Lowen fuzzy compactness.Further a characterization of fuzzy metacompactness in the weakly inducedL-topological spaces is also obtained.

We study new sequence spaces associated to sequences in normed spaces and the band matrix F̂ defined by the Fibonacci sequence. We give some characterizations of continuous linear operators and weakly unconditionally Cauchy series by means of completeness of the new sequence spaces. Also, we characterize the barreledness of a normed space via weakly∗ unconditionally Cauchy series in [Formula: se...

This chapter introduces the notion which is main interest in this book and responsible for title. Locally mixed symmetric spaces are a very natural construction enrich of locally spaces, studied Chap. 2. While there pair data entering, \((G_{\mathbb Q}, {\varGamma })\), where \(G_{\mathbb Q}\) semisimple \({\mathbb Q}\)-group such that \(X=G_{\mathbb R}/K\) space non-compact type maximal compac...