% problem-set/topology/point.set/lemma4.clauses
% created : 08/08/88
% revised : 08/17/89

% description : 
% 
% lemma: If yt is the subspace topology for y a subspace of x,
% 	under topology xt, then (y,yt) is a topological space.

% representation : 
%
% See axioms.decl for a full explanation.

% denial: exists Y such that under the subspace topology Y does
% 	not form a topological space.

top_space(X,T).
subset(Y,X).
-top_space(Y,subspace_top(X,T,Y)).