Ideal in topological spaces have been considered since 1930. This topic won its importance by
the paper of Vaidyanathaswamy [7] and Kuratwoski [6]. Applications to various fields were further
investigated by Jankovi? and Hamlett [3]; Dontchev et al. [2]; Mukherjee et al. [4]; Arenas et al. [5];
Navaneethakrishnan et al. [1]; Nasef and Mahmoud [8], etc. In this paper We used only the proper ideal
to work , ideal bace, turing point, finer than, and maximal ideal to prove continuous, compactness, ????
space and ideal net. Let ???? , ???? be a topological space, by ???? we will denote the open neighborhood
system at a point ?? ?? ??.
A set ? is said to be directed if and only if there is a relation ?? on ? satisfying, (i) ?? ?? ?? for each
?? ?? ?, (ii) if ???? ?? ???? and ???? ?? ???? then ???? ?? ????, (iii) if ????, ???? ?? ?, then there is ???? ?? ? such that
???? ?? ???? and ???? ?? ???? [9]. A net in a set ?? is a function ?? on a directed set into ?? [9]. By ????????????? we
will denote the net ??. Let ?? ?? ??, a net ?? on ?? is said to be eventually in ?? iff there exists ???? ?? ? such
that ?? ?? ???? implies that ???? ?? ??. A net ????????????? convergent to ???? ?? ?? iff its eventually for each
?? ?? ?????? and denoted by ????????????? ?? ????. A topological space ?? is compact if and only if every class ????????
of closed subsets of ?? which satisfies the finite intersection has, itself, a non-empty intersection [9]