Let X be a topological space and let Y be a subset of X. Check that the so-called subspace topology is indeed a topology on Y.© BrainMass Inc. brainmass.com December 24, 2021, 5:10 pm ad1c9bdddf
Definition of Topological Space: Suppose X is any non-empty set. Let T be a set of subsets of X such that the following are satisfied.
i) The empty set is in T i.e. and the set X is in T i.e.
ii) Arbitrary union of elements of T is an element of T i.e. where I is an index set and
iii) Finite intersection of elements of T is an element of T i.e. where , ( - the set of natural numbers) and
Then we say that ...
The solution to a topological space problem is explained in detail. The response received a rating of "5" from the student who posted the question.