It is shown that a commutative reduced ring R is a Baer ring if and only if it is a CS-ring; if and only if every dense subset of Spec (R) containing Max (R) is an extremally disconnected space; if and only if every non-zero ideal of R is essential in a principal ideal generated by an idempotent.

Let A be a bounded linear operator on a Banach space X. We investigate the conditions of existing rank-one operator B such that I+f(A)B is invertible for every analytic function f on sigma(A). Also we compare the invariant subspaces of f(A)B and B. This work is motivated by an operator method on the Banach space ell^2 for solving some PDEs which is extended to general operator space under some ...

Based on previous results that study the completion of fuzzy metric spaces, we show that every intuitionistic fuzzy quasi-metric space, using the notion of fuzzy metric space in the sense of Kramosil and Michalek to obtain a generalization to the quasi-metric setting, has a bicompletion which is unique up to isometry.

In this paper, a new method was proposed for the navigation of a mobile robot in an unknown dynamic environment. The robot could detect only a limited radius of its surrounding with its sensors and it went on the shortest null space (SNS) toward the goal. In the case of no obstacle, SNS was a direct path from the robot to goal; however, in the presence of obstacles, SNS was a space around the r...

 In Proposition 2.6 in (G‎. ‎Gruenhage‎, ‎A‎. ‎Lutzer‎, ‎Baire and Volterra spaces‎, ‎textit{Proc‎. ‎Amer‎. ‎Math‎. ‎Soc.} {128} (2000)‎, ‎no‎. ‎10‎, ‎3115--3124) a condition that‎ ‎every point of $D$ is $G_delta$ in $X$ was overlooked‎. ‎So we‎ ‎proved some conditions by which a Baire space is equivalent to a‎ ‎Volterra space‎. ‎In this note we show that if $X$ is a‎ ‎monotonically normal $T_1...

In this paper, a new method was proposed for the navigation of a mobile robot in an unknown dynamic environment. The robot could detect only a limited radius of its surrounding with its sensors and it went on the shortest null space (SNS) toward the goal. In the case of no obstacle, SNS was a direct path from the robot to goal; however, in the presence of obstacles, SNS was a space around the r...