Spelling corrections

A number of spelling corrections as reported by the codespell (see: https://github.com/codespell-project/codespell) program and lists.

Some remarks:
- not considered are grammatical errors
- not considered are names in the code although there are a number that could be improved (like `childs` -> `children`)
- in the documentation it could be made clearer what are variables and what is running text (e.g. by placing variables in running text between backticks)
- some comments are in the French language, I think it would be better to have them in the English (United States version).

2 files changed, 3 insertions, 3 deletions

diff --git a/src/common/include/gudhi/reader_utils.h b/src/common/include/gudhi/reader_utils.h
index 29d5423d..a7d82541 100644
--- a/src/common/include/gudhi/reader_utils.h
+++ b/src/common/include/gudhi/reader_utils.h
@@ -231,7 +231,7 @@ std::vector<std::vector<Filtration_value>> read_lower_triangular_matrix_from_csv
 
   std::string line;
 
-  // the first line is emtpy, so we ignore it:
+  // the first line is empty, so we ignore it:
   std::getline(in, line);
   std::vector<Filtration_value> values_in_this_line;
   result.push_back(values_in_this_line);
diff --git a/src/common/include/gudhi/writing_persistence_to_file.h b/src/common/include/gudhi/writing_persistence_to_file.h
index 2e36b831..3a0df1a8 100644
--- a/src/common/include/gudhi/writing_persistence_to_file.h
+++ b/src/common/include/gudhi/writing_persistence_to_file.h
@@ -48,7 +48,7 @@ class Persistence_interval_common {
       : birth_(birth), death_(death), dimension_(dim), arith_element_(field) {}
 
   /**
-   * Operator to compare two persistence pairs. During the comparision all the
+   * Operator to compare two persistence pairs. During the comparison all the
    * fields: birth, death, dimensiona and arith_element_ are taken into account
    * and they all have to be equal for two pairs to be equal.
   **/
@@ -65,7 +65,7 @@ class Persistence_interval_common {
   /**
    * Operator to compare objects of a type Persistence_interval_common.
    * One intervals is smaller than the other if it has lower persistence.
-   * Note that this operator do not take Arith_element into account when doing comparisions.
+   * Note that this operator do not take Arith_element into account when doing comparisons.
   **/
   bool operator<(const Persistence_interval_common& i2) const {
     return fabs(this->death_ - this->birth_) < fabs(i2.death_ - i2.birth_);