In this paper, we study the behavior of some topological and cardinal properties of topological spaces under the influence of the Nτφ -kernel of a space X. It has been proved that the Nτφ-kernel of a ...space X preserves the density and the network π - weight of normal spaces. Besides, shown that the N-compact kernel of a space X preserves the Souslin properties, the weight, the density, and the π -network weight of normal spaces.
In this work, the caliber of the space of subtle (thin) complete coupled (linked) systems of a topological space is studied. It is proved that an infinite cardinal
is a caliber for the space of ...subtle complete coupled systems
of an infinite compact space
, if and only if when cardinal
is a caliber for a subtle superextension
of the space
. The weight and the Souslin number of the
-kernel of the space
are also studied. It is shown that the weight of an infinite compact space
coincides with the weight of the
-kernel of the space
. It was also proved that the Souslin number of an infinite compact space
coincides with the Souslin number of the
-kernel of the space
.
In this paper, we study the behavior of some topological and cardinal properties of topological spaces under the influence of the
-kernel of a topological space
. It has been proved that the
-kernel ...of a topological space
preserves the density and the network
-weight of normal spaces.
In this work, the separability, locally separability, weakly separability and locally weakly separability of the space of probability measures of an infinite compact space are studied. It is proved ...that an infinite compact space
is a separable (locally separable), if and only if the space
is a separable (locally separable). It was also proved that, if a space
is a weakly separable (locally weakly separable), then the space
is a weakly separable (locally weakly separable).
In this paper the network-type properties (network,cs−network,cs∗−network,cn−network andck−network) of the spaceSPnGXofG-permutation degree ofXare studied. It is proved that:(1) IfXis aT1-space that ...has a network of cardinality≤κ, thenSPnGXhas a network of cardinality≤κ;(2) IfXis aT1-space that has acs-network (resp.cs∗-network) ofcardinality≤κ, thenSPnGXhas acs-network (resp.cs∗-network) ofcardinality≤κ;(3) IfXis aT1-space that has acn-network (resp.ck-network) ofcardinality≤κ, thenSPnGXhas acn-network (resp.ck−network) ofcardinality≤κ.
PDF
