vi. oldal
at the end of the 19th and the beginning of the 20th centuries by A. Liapunov, E. Schmidt, A. Nekrasov and others.

4. oldal
0. That is, if {x} is a relatively open subset of A. A set is perfect if and only if it is closed and has no isolated points. Note that if A has no isolated...

5. oldal
Let X and Y be topological spaces and let f : X ‘—¿ Y be a mapping. The following assertions are equivalent: (a) The mapping f is continuous. (b)...

6. oldal
Every family of closed subsets of X with the finite intersection property has a nonempty intersection. (c) Every net in X has a limit point (or,

4. oldal
C A). That is, • A set is closed if and only if it contains all its limit points. To illustrate

2. oldal
x. The complement of an open set is a closed set. A set that is both closed and open is called a clopen set. A set may be both open and closed, or it may...

59. oldal
is a constant function on U. Therefore, for complex-valued functions, the strong maximum modulus theorem holds. However, this is not the case in general...

1. oldal
Spaces Let X be a set. A topology on X is a collection T of subsets of

11. oldal
are allowed). To see this, note that every point in an open set must be contained in a maximal open interval, every open interval contains a rational number,...

125. oldal
By passing to a subsequence, if necessary, we may assume that the sequences of integers