We prove that a space is quotient π-image of a locally separable metric space if and only if it has a πand double cs∗cover. We also investigate quotient π-s-images of locally separable metric spaces.

We provide examples of non-locally compact geodesic Ptolemy metric spaces which are not uniquely geodesic. On the other hand, we show that locally compact, geodesic Ptolemy metric spaces are uniquely geodesic. Moreover, we prove that a metric space is CAT(0) if and only if it is Busemann convex and Ptolemy.

We show that two of the Bryant-Salamon G2-manifolds have a simple topology, S \S or S \CP . In this connection, we show there exists a complete Ricci-flat (non-flat) metric on Sn \ Sm for some n − 1 > m. We also give many examples of special Lagrangian submanifolds of T ∗Sn with the Stenzel metric. Hypersurface geometry is essential for these arguments.

We show that two of Bryant-Salamon’s G2-manifolds have a simple topology, S \ S or S \ CP . In this connection, we show there exists a complete Ricci-flat (non-flat) metric on Sn \ Sm for some n − 1 > m. We also give many examples of special Lagrangian submanifolds of T ∗Sn with the Stenzel metric. The hypersurface geometry is essential in the argument.

We characterize sequence-covering (resp., 1-sequence-covering, 2-sequence-covering) mssc-images of locally separable metric spaces by means of σ-locally finite cs-networks (resp., sn-networks, so-networks) consisting of א0-spaces (resp., sn-second countable spaces, so-second countable spaces). As the applications, we get characterizations of certain sequence-covering, quotient mssc-images of lo...

Abstract It is well-known that the dimension of optimal anticodes in rank-metric divisible by maximum m between number rows and columns matrices. Moreover, for a fixed k , are codes with least rank, among those . In this paper, we study family whose not rank possible dimension, according to Anticode bound. As these anticodes, call them quasi (qOACs). addition, dually qOAC dual also qOAC. We des...

In this paper, we characterize pseudo-sequence-covering π-images of locally separable metric spaces by means of fcs-covers and point-star networks. We also investigate pseudo-sequence-covering π-s-images of locally separable metric spaces.

The object of the present paper is to study locally φsymmetric LP-Sasakian manifolds admitting semi-symmetric metric connection and obtain a necessary and sufficient condition for a locally φsymmetric LP-Sasakian manifold with respect to semi-symmetric metric connection to be locally φ-symmetric LP-Sasakian manifold with respect to Levi-Civita connection. AMS Mathematics Subject Classification ...

We show that there exist non-trivial PL knots S n−2 ⊂ S n , n ≥ 5, whose complements have the homotopy type of circles. This is in contrast to the case of smooth, PL locally-flat, and topological locally-flat knots, for which it is known that if the complement has the homotopy type of a circle, then the knot is trivial. It is well-known that if the complement of a smooth, PL locally-flat, or to...