The open-open topology for function spaces

Sequential Properties of Function Spaces with the Compact-open Topology

Let M be the countably infinite metric fan. We show that Ck(M, 2) is sequential and contains a closed copy of Arens space S2. It follows that if X is metrizable but not locally compact, then Ck(X) contains a closed copy of S2, and hence does not have the property AP. We also show that, for any zero-dimensional Polish space X, Ck(X, 2) is sequential if and only if X is either locally compact or ...

Investigating the Effective Indicators on the Desirable Quality of Open and Semi-Open Spaces of Contemporary Housingry Housing

Today’s housing, as a private realm of human life, has changed in comparison with the past which was made regardless of quality, desirability, and lack of paying attention to the human needs and its psychological consequences; That is to say, residential units have turned into a set of closed spaces and their open and semi-open spaces have been merged into the urban spaces which disrupted their...

Explaining the effective features of open and semi-open spaces in availability and increase of social interactions in residential complexes

By increasing house demand for living, the urban development planning has turned to towers, which provides a platform for the growth of the city, regardless of the traditional Iranian's architecture. Among the vital elements in traditional architecture, there are a variety of open and semi-open spaces such as the central courtyard, pool, veranda, balcony, etc that have been provided the needs f...

Open Problems in Topology

Open problems for equienergetic graphs

The energy of a graph is equal to the sum of the absolute values of its eigenvalues. Two graphs of the same order are said to be equienergetic if their energies are equal. We point out the following two open problems for equienergetic graphs. (1) Although it is known that there are numerous pairs of equienergetic, non-cospectral trees, it is not known how to systematically construct any such pa...