It is shown that the space X[0,1], of continuous maps [0, 1] X with the compact-open topology, is not locally compact for any space X having a nonconstant path of closed points. ...
In the early 1920s, Pavel Urysohn proved his famous lemma (sometimes referred to as "first non-trivial result of point set topology"). Among other applications, this lemm...
The paper presents a new set of axioms of digital topology, which are easily understandable for application developers. They define a class of locally finite (LF) topological space...
In this paper we show that complex (scale-free) network topologies naturally emerge from hyperbolic metric spaces. The hyperbolic geometry can be used to facilitate maximally efï¬...
Fragkiskos Papadopoulos, Dmitri V. Krioukov, Mari&...
We present a Stone duality for bitopological spaces in analogy to the duality between topological spaces and frames, and discuss the resulting notions of sobriety and spatiality. ...