The notion of generalized locally bounded I-TOPOLOGICAL VECTOR SPACES is introduced. Some of their important properties are studied. The relationship between this kind of SPACES and the locally bounded I-TOPOLOGICAL VECTOR SPACES introduced by Wu and Fang [Boundedness and locally bounded fuzzy TOPOLOGICAL VECTOR SPACES, Fuzzy Math. 5 (4) (1985) 87-94] is discussed. Moreover, we also use the family of generalized fuzzy quasi-norms to characterize the generalized locally bounded I-TOPOLOGICAL VECTOR SPACES, and give some applications of this characterization.

In this paper, we have defined and studied a generalized form of TOPOLOGICAL VECTOR SPACES called s-TOPOLOGICAL VECTOR SPACES. s-TOPOLOGICAL VECTOR SPACES are defined by using semi-open sets and semi-continuity in the sense of Levine. Along with other results, it is proved that every s-TOPOLOGICAL VECTOR space is generalized homogeneous space. Every open subspace of an s-TOPOLOGICAL VECTOR space is an s-TOPOLOGICAL VECTOR space. A homomorphism between s-TOPOLOGICAL VECTOR SPACES is semi-continuous if it is s-continuous at the identity.

In this paper, a new definition of fuzzy bounded sets and totally fuzzy bounded sets is introduced and properties of such sets are studied. Then a relation between totally fuzzy bounded sets and N-compactness is discussed. Finally, a geometric characterization for fuzzy totally bounded sets in I- TOPOLOGICAL VECTOR SPACES is derived.

In this corrigenda, we have pointed out that Example 2.7, Corollary 3.7 and Corollary 5.3 in the paper: $\omega b-$TOPOLOGICAL VECTOR SPACES, WSEAS Trans. Math. 19 (2020), $119-132$, by Latif are incorrect. We have also presented the corrected version of these results. Furthermore, we introduce and study some new classes of TOPOLOGICAL VECTOR SPACES.

In this article we study the existence of non-continuous linear functionals on TOPOLOGICAL VECTOR SPACES. Both sufficient and necessary conditions for the existence of such maps are found.

A new definition of boundedness of linear order-homomorphisms (LOH) inL-TOPOLOGICAL VECTOR SPACES is proposed. The new definition is compared with the previous one given by Fang [The continuity of fuzzy linear order-homomorphism, J. Fuzzy Math.5 (4) (1997) 829-838]. In addition, the relationship between boundedness and continuity of LOHs is discussed.Finally, a new uniform boundedness principle in L-TOPOLOGICAL VECTOR SPACES is established in the sense of a new definition of uniform boundedness for a family of LOHs.