Locally planar Peano continua admitting continuous decomposition into pseudo-arcs (into acyclic curves) are characterized as those with no local separating point. This extends the well-known result of Lewis and Walsh on a continuous decomposition of the plane into pseudo-arcs.
A compact metric space X̃ is said to be a continuous pseudo-hairy space over a compact space X ⊂ X̃ provided there exists an open, monotone retraction such that all fibers are pseudo-arcs and any continuum in X̃ joining two different fibers of r intersects X. A continuum is called a continuous pseudo-fan of a compactum X if there are a point and a family ℱ of pseudo-arcs such that , any subcontinuum of intersecting two different elements of ℱ contains c, and ℱ is homeomorphic to X (with...
This paper introduces partial tvs-cone metric spaces as a common generalization of both tvs-cone metric spaces and partial metric spaces, and gives a new fixed point theorem for contractions of Nadler type on partial tvs-cone metric spaces. As corollaries, we obtain the main results of S. B. Nadler (1969), D. Wardowski (2011), S. Radenović et al. (2011) and H. Aydi et al. (2012) are deduced.
Let be a compact Hausdorff space with a point such that is linearly Lindelöf. Is then first countable at ? What if this is true for every in ? We consider these and some related questions, and obtain partial answers; in particular, we prove that the answer to the second question is “yes” when is, in addition, -monolithic. We also prove that if is compact, Hausdorff, and is strongly discretely Lindelöf, for every in , then is first countable. An example of linearly Lindelöf...