A rectifying curve in the Euclidean $n$-space $\mathbb{E}^n$ is defined as an arc-length parametrized $\gamma$ such that its position vector always lies space (i.e., orthogonal complement of principal normal field) $\mathbb{E}^n$. In this paper, analogy to this, we introduce notion $f$-rectifying a by $s$ $f$-position field $\gamma_f$, $\gamma_f(s) = \int f(s) d\gamma$, $\mathbb{E}^n$, where $f...

In this paper, we present a constructive description of the function space all real-valued functions on R(F(R,R)) by presenting partition it into 28 distinct blocks and closed-form formula for representative each them. Each block contains elements that share common features in terms cardinality their sets continuity differentiability. Alongside classification, introduce concept Connection, whic...

In this paper, by using a special family of filters $mathcal{F}$ on an EQ-algebra $E$, we construct a topology $mathcal{T}_{mathcal{mathcal{F}}}$ on $E$ and show that $(E,mathcal{T}_{mathcal{F}})$ is a topological EQ-algebra. First of all, we give some properties of topological EQ-algebras and investigate the interaction of topological EQ-algebras and quotient topological EQ-algebras. Then we o...

We define the ε∞-product of a Banach space G by a quotient bornological space E | F that we denote by Gε∞(E | F ), and we prove that G is an L∞-space if and only if the quotient bornological spaces Gε∞(E | F ) and (GεE) | (GεF ) are isomorphic. Also, we show that the functor .ε∞. : Ban× qBan −→ qBan is left exact. Finally, we define the ε∞-product of a b-space by a quotient bornological space a...